diff --git a/packages/patterns/index.js b/packages/patterns/index.js
index b32e6ea809..d93b0483a2 100644
--- a/packages/patterns/index.js
+++ b/packages/patterns/index.js
@@ -73,6 +73,7 @@ export {
   getInterfaceGuardPayload,
   getInterfaceMethodKeys,
 } from './src/patterns/getGuardPayloads.js';
+export { mustCompress, mustDecompress } from './src/patterns/compress.js';
 
 // eslint-disable-next-line import/export
 export * from './src/types.js';
diff --git a/packages/patterns/src/patterns/compress.js b/packages/patterns/src/patterns/compress.js
new file mode 100644
index 0000000000..4c07f8237f
--- /dev/null
+++ b/packages/patterns/src/patterns/compress.js
@@ -0,0 +1,292 @@
+// @ts-nocheck So many errors that the suppressions hamper readability.
+// TODO fix and then turn at-ts-check back on
+import {
+  assertChecker,
+  makeTagged,
+  passStyleOf,
+  recordNames,
+  recordValues,
+} from '@endo/marshal';
+import {
+  kindOf,
+  assertPattern,
+  maybeMatchHelper,
+  matches,
+  checkMatches,
+  mustMatch,
+} from './patternMatchers.js';
+import { isKey } from '../keys/checkKey.js';
+import { keyEQ } from '../keys/compareKeys.js';
+
+/** @import {Compress, Decompress, MustCompress, MustDecompress} from '../types.js' */
+
+const { fromEntries } = Object;
+const { Fail, quote: q } = assert;
+
+const isNonCompressingMatcher = pattern => {
+  const patternKind = kindOf(pattern);
+  if (patternKind === undefined) {
+    return false;
+  }
+  const matchHelper = maybeMatchHelper(patternKind);
+  return matchHelper && matchHelper.compress === undefined;
+};
+
+/**
+ * When, for example, all the specimens in a given store match a
+ * specific pattern, then each of those specimens must contain the same
+ * literal superstructure as their one shared pattern. Therefore, storing
+ * that literal superstructure would be redumdant. If `specimen` does
+ * match `pattern`, then `compress(specimen, pattern)` will return a bindings
+ * array which is hopefully more compact than `specimen` as a whole, but
+ * carries all the information from specimen that cannot be derived just
+ * from knowledge that it matches this `pattern`.
+ *
+ * @type {Compress}
+ */
+const compress = (specimen, pattern) => {
+  if (isNonCompressingMatcher(pattern)) {
+    if (matches(specimen, pattern)) {
+      return harden({ compressed: specimen });
+    }
+    return undefined;
+  }
+
+  // Not yet frozen! Used to accumulate bindings
+  const bindings = [];
+  const emitBinding = binding => {
+    bindings.push(binding);
+  };
+  harden(emitBinding);
+
+  /**
+   * @param {Passable} innerSpecimen
+   * @param {Pattern} innerPattern
+   * @returns {boolean}
+   */
+  const compressRecur = (innerSpecimen, innerPattern) => {
+    assertPattern(innerPattern);
+    if (isKey(innerPattern)) {
+      return keyEQ(innerSpecimen, innerPattern);
+    }
+    const patternKind = kindOf(innerPattern);
+    const specimenKind = kindOf(innerSpecimen);
+    switch (patternKind) {
+      case undefined: {
+        return false;
+      }
+      case 'copyArray': {
+        if (
+          specimenKind !== 'copyArray' ||
+          innerSpecimen.length !== innerPattern.length
+        ) {
+          return false;
+        }
+        return innerPattern.every((p, i) => compressRecur(innerSpecimen[i], p));
+      }
+      case 'copyRecord': {
+        if (specimenKind !== 'copyRecord') {
+          return false;
+        }
+        const specimenNames = recordNames(innerSpecimen);
+        const pattNames = recordNames(innerPattern);
+
+        if (specimenNames.length !== pattNames.length) {
+          return false;
+        }
+        const specimenValues = recordValues(innerSpecimen, specimenNames);
+        const pattValues = recordValues(innerPattern, pattNames);
+
+        return pattNames.every(
+          (name, i) =>
+            specimenNames[i] === name &&
+            compressRecur(specimenValues[i], pattValues[i]),
+        );
+      }
+      case 'copyMap': {
+        if (specimenKind !== 'copyMap') {
+          return false;
+        }
+        const {
+          payload: { keys: pattKeys, values: valuePatts },
+        } = innerPattern;
+        const {
+          payload: { keys: specimenKeys, values: specimenValues },
+        } = innerSpecimen;
+        // TODO BUG: this assumes that the keys appear in the
+        // same order, so we can compare values in that order.
+        // However, we're only guaranteed that they appear in
+        // the same rankOrder. Thus we must search one of these
+        // in the other's rankOrder.
+        if (!keyEQ(specimenKeys, pattKeys)) {
+          return false;
+        }
+        return compressRecur(specimenValues, valuePatts);
+      }
+      default:
+        {
+          const matchHelper = maybeMatchHelper(patternKind);
+          if (matchHelper) {
+            if (matchHelper.compress) {
+              const subCompressedRecord = matchHelper.compress(
+                innerSpecimen,
+                innerPattern.payload,
+                compress,
+              );
+              if (subCompressedRecord === undefined) {
+                return false;
+              } else {
+                emitBinding(subCompressedRecord.compressed);
+                return true;
+              }
+            } else if (matches(innerSpecimen, innerPattern)) {
+              assert(isNonCompressingMatcher(innerPattern));
+              emitBinding(innerSpecimen);
+              return true;
+            } else {
+              return false;
+            }
+          }
+        }
+        throw Fail`unrecognized kind: ${q(patternKind)}`;
+    }
+  };
+
+  if (compressRecur(specimen, pattern)) {
+    return harden({ compressed: bindings });
+  } else {
+    return undefined;
+  }
+};
+harden(compress);
+
+/**
+ * `mustCompress` is to `compress` approximately as `mustMatch` is to `matches`.
+ * Where `compress` indicates pattern match failure by returning `undefined`,
+ * `mustCompress` indicates pattern match failure by throwing an error
+ * with a good pattern-match-failure diagnostic. Thus, like `mustMatch`,
+ * `mustCompress` has an additional optional `label` parameter to be used on
+ * the outside of that diagnostic if needed. If `mustCompress` does return
+ * normally, then the pattern match succeeded and `mustCompress` returns a
+ * valid compressed value.
+ *
+ * @type {MustCompress}
+ */
+export const mustCompress = (specimen, pattern, label = undefined) => {
+  const compressedRecord = compress(specimen, pattern);
+  if (compressedRecord !== undefined) {
+    return compressedRecord.compressed;
+  }
+  // `compress` is validating, so we don't need to redo all of `mustMatch`.
+  // We use it only to generate the error.
+  // Should only throw
+  checkMatches(specimen, pattern, assertChecker, label);
+  throw Fail`internal: ${label}: inconsistent pattern match: ${q(pattern)}`;
+};
+harden(mustCompress);
+
+/**
+ * `decompress` reverses the compression performed by `compress`
+ * or `mustCompress`, in order to recover the equivalent
+ * of the original specimen from the `bindings` array and the `pattern`.
+ *
+ * @type {Decompress}
+ */
+const decompress = (compressed, pattern) => {
+  if (isNonCompressingMatcher(pattern)) {
+    return compressed;
+  }
+
+  assert(Array.isArray(compressed));
+  passStyleOf(compressed) === 'copyArray' ||
+    Fail`Pattern ${pattern} expected bindings array: ${compressed}`;
+  let i = 0;
+  const takeBinding = () => {
+    i < compressed.length ||
+      Fail`Pattern  ${q(pattern)} expects more than ${q(
+        compressed.length,
+      )} bindings: ${compressed}`;
+    const binding = compressed[i];
+    i += 1;
+    return binding;
+  };
+  harden(takeBinding);
+
+  const decompressRecur = innerPattern => {
+    assertPattern(innerPattern);
+    if (isKey(innerPattern)) {
+      return innerPattern;
+    }
+    const patternKind = kindOf(innerPattern);
+    switch (patternKind) {
+      case undefined: {
+        throw Fail`decompress expected a pattern: ${q(innerPattern)}`;
+      }
+      case 'copyArray': {
+        return harden(innerPattern.map(p => decompressRecur(p)));
+      }
+      case 'copyRecord': {
+        const pattNames = recordNames(innerPattern);
+        const pattValues = recordValues(innerPattern, pattNames);
+        const entries = pattNames.map((name, j) => [
+          name,
+          decompressRecur(pattValues[j]),
+        ]);
+        // Reverse so printed form looks less surprising,
+        // with ascenting rather than descending property names.
+        return harden(fromEntries(entries.reverse()));
+      }
+      case 'copyMap': {
+        const {
+          payload: { keys: pattKeys, values: valuePatts },
+        } = innerPattern;
+        return makeTagged(
+          'copyMap',
+          harden({
+            keys: pattKeys,
+            values: valuePatts.map(p => decompressRecur(p)),
+          }),
+        );
+      }
+      default:
+        {
+          const matchHelper = maybeMatchHelper(patternKind);
+          if (matchHelper) {
+            if (matchHelper.decompress) {
+              const subCompressed = takeBinding();
+              return matchHelper.decompress(
+                subCompressed,
+                innerPattern.payload,
+                decompress,
+              );
+            } else {
+              assert(isNonCompressingMatcher(innerPattern));
+              return takeBinding();
+            }
+          }
+        }
+        throw Fail`unrecognized pattern kind: ${q(patternKind)} ${q(
+          innerPattern,
+        )}`;
+    }
+  };
+
+  return decompressRecur(pattern);
+};
+harden(decompress);
+
+/**
+ * `decompress` reverses the compression performed by `compress`
+ * or `mustCompress`, in order to recover the equivalent
+ * of the original specimen from `compressed` and `pattern`.
+ *
+ * @type {MustDecompress}
+ */
+export const mustDecompress = (compressed, pattern, label = undefined) => {
+  const value = decompress(compressed, pattern);
+  // `decompress` does some checking, but is not validating, so we
+  // need to do the full `mustMatch` here to validate as well as to generate
+  // the error if invalid.
+  mustMatch(value, pattern, label);
+  return value;
+};
diff --git a/packages/patterns/src/patterns/patternMatchers.js b/packages/patterns/src/patterns/patternMatchers.js
index 0aa27ec4e4..99ce409ee5 100644
--- a/packages/patterns/src/patterns/patternMatchers.js
+++ b/packages/patterns/src/patterns/patternMatchers.js
@@ -33,17 +33,25 @@ import {
   checkCopyBag,
   getCopyMapEntryArray,
   makeCopyMap,
+  makeCopySet,
+  makeCopyBag,
 } from '../keys/checkKey.js';
 import { generateCollectionPairEntries } from '../keys/keycollection-operators.js';
 
 /**
  * @import {Checker, CopyRecord, CopyTagged, Passable} from '@endo/pass-style'
- * @import {ArgGuard, AwaitArgGuard, CheckPattern, GetRankCover, InterfaceGuard, MatcherNamespace, MethodGuard, MethodGuardMaker, Pattern, RawGuard, SyncValueGuard, Kind, Limits, AllLimits, Key, DefaultGuardType} from '../types.js'
+ * @import {ArgGuard, AwaitArgGuard, CheckPattern, GetRankCover, InterfaceGuard, MatcherNamespace, MethodGuard, MethodGuardMaker, Pattern, RawGuard, SyncValueGuard, Kind, Compress, Decompress, Limits, AllLimits, Key, DefaultGuardType} from '../types.js'
  * @import {MatchHelper, PatternKit} from './types.js'
  */
 
 const { entries, values } = Object;
-const { ownKeys } = Reflect;
+const { ownKeys, apply } = Reflect;
+
+// TODO simplify once we can assume Object.hasOwn everywhere. This probably
+// means, when we stop supporting Node 14.
+const { hasOwnProperty } = Object.prototype;
+const hasOwn =
+  Object.hasOwn || ((obj, name) => apply(hasOwnProperty, obj, [name]));
 
 /** @type {WeakSet<Pattern>} */
 const patternMemo = new WeakSet();
@@ -760,6 +768,44 @@ const makePatternKit = () => {
     );
   };
 
+  /**
+   * @param {Passable[]} array
+   * @param {Pattern} patt
+   * @param {Compress} compress
+   * @returns {Passable[] | undefined}
+   */
+  const arrayCompressMatchPattern = (array, patt, compress) => {
+    if (isKind(patt, 'match:any')) {
+      return array;
+    }
+    const bindings = [];
+    for (const el of array) {
+      const subCompressedRecord = compress(el, patt);
+      if (subCompressedRecord) {
+        bindings.push(subCompressedRecord.compressed);
+      } else {
+        return undefined;
+      }
+    }
+    return harden(bindings);
+  };
+
+  /**
+   * @param {Passable} compressed
+   * @param {Pattern} patt
+   * @param {Decompress} decompress
+   * @returns {Passable[]}
+   */
+  const arrayDecompressMatchPattern = (compressed, patt, decompress) => {
+    if (!Array.isArray(compressed)) {
+      throw Fail`Compressed array must be an array: ${compressed}`;
+    }
+    if (isKind(patt, 'match:any')) {
+      return compressed;
+    }
+    return harden(compressed.map(subBindings => decompress(subBindings, patt)));
+  };
+
   // /////////////////////// Match Helpers /////////////////////////////////////
 
   /** @type {MatchHelper} */
@@ -777,12 +823,31 @@ const makePatternKit = () => {
 
   /** @type {MatchHelper} */
   const matchAndHelper = harden({
-    tag: 'match:and',
+    tag: 'match:and:1',
 
     checkMatches: (specimen, patts, check) => {
       return patts.every(patt => checkMatches(specimen, patt, check));
     },
 
+    // Compress only according to the last conjunct
+    compress: (specimen, patts, compress) => {
+      const { length } = patts;
+      // We know there are at least two patts
+      const lastPatt = patts[length - 1];
+      const allButLast = patts.slice(0, length - 1);
+      if (
+        !allButLast.every(patt => checkMatches(specimen, patt, identChecker))
+      ) {
+        return undefined;
+      }
+      return compress(specimen, lastPatt);
+    },
+
+    decompress: (compressed, patts, decompress) => {
+      const lastPatt = patts[patts.length - 1];
+      return decompress(compressed, lastPatt);
+    },
+
     checkIsWellFormed: (allegedPatts, check) => {
       const checkIt = patt => checkPattern(patt, check);
       return (
@@ -804,7 +869,7 @@ const makePatternKit = () => {
 
   /** @type {MatchHelper} */
   const matchOrHelper = harden({
-    tag: 'match:or',
+    tag: 'match:or:1',
 
     checkMatches: (specimen, patts, check) => {
       const { length } = patts;
@@ -829,6 +894,31 @@ const makePatternKit = () => {
       return check(false, X`${specimen} - Must match one of ${q(patts)}`);
     },
 
+    // Compress to an array pair of the index of the
+    // first disjunct that succeeded, and the compressed according to
+    // that disjunct.
+    compress: (specimen, patts, compress) => {
+      assert(Array.isArray(patts)); // redundant. Just for type checker.
+      const { length } = patts;
+      if (length === 0) {
+        return undefined;
+      }
+      for (let i = 0; i < length; i += 1) {
+        const subCompressedRecord = compress(specimen, patts[i]);
+        if (subCompressedRecord !== undefined) {
+          return harden({ compressed: [i, subCompressedRecord.compressed] });
+        }
+      }
+      return undefined;
+    },
+
+    decompress: (compressed, patts, decompress) => {
+      (Array.isArray(compressed) && compressed.length === 2) ||
+        Fail`Or compression must be a case index and a compression by that case: ${compressed}`;
+      const [i, subCompressed] = compressed;
+      return decompress(harden(subCompressed), patts[i]);
+    },
+
     checkIsWellFormed: matchAndHelper.checkIsWellFormed,
 
     getRankCover: (patts, encodePassable) =>
@@ -926,7 +1016,7 @@ const makePatternKit = () => {
 
   /** @type {MatchHelper} */
   const matchTaggedHelper = harden({
-    tag: `match:tagged`,
+    tag: `match:tagged:1`,
 
     checkMatches: (specimen, [tagPatt, payloadPatt], check) => {
       if (passStyleOf(specimen) !== 'tagged') {
@@ -943,6 +1033,35 @@ const makePatternKit = () => {
       );
     },
 
+    compress: (specimen, [tagPatt, payloadPatt], compress) => {
+      if (passStyleOf(specimen) === 'tagged') {
+        const compressedTagRecord = compress(getTag(specimen), tagPatt);
+        if (!compressedTagRecord) {
+          return undefined;
+        }
+        const compressedPayloadRecord = compress(specimen.payload, payloadPatt);
+        if (!compressedPayloadRecord) {
+          return undefined;
+        }
+        return harden({
+          compressed: [
+            compressedTagRecord.compressed,
+            compressedPayloadRecord.compressed,
+          ],
+        });
+      }
+      return undefined;
+    },
+
+    decompress: (compressed, [tagPatt, payloadPatt], decompress) => {
+      (Array.isArray(compressed) && compressed.length === 2) ||
+        Fail`tagged compression must be a pair ${compressed}`;
+      const [compressedTag, compressedPayload] = compressed;
+      const tag = decompress(compressedTag, tagPatt);
+      const payload = decompress(compressedPayload, payloadPatt);
+      return makeTagged(tag, payload);
+    },
+
     checkIsWellFormed: (payload, check) =>
       checkMatches(
         payload,
@@ -1238,7 +1357,7 @@ const makePatternKit = () => {
 
   /** @type {MatchHelper} */
   const matchArrayOfHelper = harden({
-    tag: `match:arrayOf`,
+    tag: `match:arrayOf:1`,
 
     checkMatches: (specimen, [subPatt, limits = undefined], check) => {
       const { arrayLengthLimit } = limit(limits);
@@ -1254,6 +1373,29 @@ const makePatternKit = () => {
       );
     },
 
+    // Compress to an array of corresponding bindings arrays
+    compress: (specimen, [subPatt, limits = undefined], compress) => {
+      const { arrayLengthLimit } = limit(limits);
+      if (
+        isKind(specimen, 'copyArray') &&
+        Array.isArray(specimen) && // redundant. just for type checker.
+        specimen.length <= arrayLengthLimit
+      ) {
+        const compressed = arrayCompressMatchPattern(
+          specimen,
+          subPatt,
+          compress,
+        );
+        if (compressed) {
+          return harden({ compressed });
+        }
+      }
+      return undefined;
+    },
+
+    decompress: (compressed, [subPatt, _limits = undefined], decompress) =>
+      arrayDecompressMatchPattern(compressed, subPatt, decompress),
+
     checkIsWellFormed: (payload, check) =>
       checkIsWellFormedWithLimit(
         payload,
@@ -1267,7 +1409,7 @@ const makePatternKit = () => {
 
   /** @type {MatchHelper} */
   const matchSetOfHelper = harden({
-    tag: `match:setOf`,
+    tag: `match:setOf:1`,
 
     checkMatches: (specimen, [keyPatt, limits = undefined], check) => {
       const { numSetElementsLimit } = limit(limits);
@@ -1283,6 +1425,28 @@ const makePatternKit = () => {
       );
     },
 
+    // Compress to an array of corresponding bindings arrays
+    compress: (specimen, [keyPatt, limits = undefined], compress) => {
+      const { numSetElementsLimit } = limit(limits);
+      if (
+        isKind(specimen, 'copySet') &&
+        /** @type {Array} */ (specimen.payload).length <= numSetElementsLimit
+      ) {
+        const compressed = arrayCompressMatchPattern(
+          specimen.payload,
+          keyPatt,
+          compress,
+        );
+        if (compressed) {
+          return harden({ compressed });
+        }
+      }
+      return undefined;
+    },
+
+    decompress: (compressed, [keyPatt, _limits = undefined], decompress) =>
+      makeCopySet(arrayDecompressMatchPattern(compressed, keyPatt, decompress)),
+
     checkIsWellFormed: (payload, check) =>
       checkIsWellFormedWithLimit(
         payload,
@@ -1296,7 +1460,7 @@ const makePatternKit = () => {
 
   /** @type {MatchHelper} */
   const matchBagOfHelper = harden({
-    tag: `match:bagOf`,
+    tag: `match:bagOf:1`,
 
     checkMatches: (
       specimen,
@@ -1326,6 +1490,46 @@ const makePatternKit = () => {
       );
     },
 
+    // Compress to an array of corresponding bindings arrays
+    compress: (
+      specimen,
+      [keyPatt, countPatt, limits = undefined],
+      compress,
+    ) => {
+      const { numUniqueBagElementsLimit, decimalDigitsLimit } = limit(limits);
+      if (
+        isKind(specimen, 'copyBag') &&
+        /** @type {Array} */ (specimen.payload).length <=
+          numUniqueBagElementsLimit &&
+        specimen.payload.every(([_key, count]) =>
+          checkDecimalDigitsLimit(count, decimalDigitsLimit, identChecker),
+        )
+      ) {
+        const compressed = arrayCompressMatchPattern(
+          specimen.payload,
+          harden([keyPatt, countPatt]),
+          compress,
+        );
+        if (compressed) {
+          return harden({ compressed });
+        }
+      }
+      return undefined;
+    },
+
+    decompress: (
+      compressed,
+      [keyPatt, countPatt, _limits = undefined],
+      decompress,
+    ) =>
+      makeCopyBag(
+        arrayDecompressMatchPattern(
+          compressed,
+          harden([keyPatt, countPatt]),
+          decompress,
+        ),
+      ),
+
     checkIsWellFormed: (payload, check) =>
       checkIsWellFormedWithLimit(
         payload,
@@ -1339,7 +1543,7 @@ const makePatternKit = () => {
 
   /** @type {MatchHelper} */
   const matchMapOfHelper = harden({
-    tag: `match:mapOf`,
+    tag: `match:mapOf:1`,
 
     checkMatches: (
       specimen,
@@ -1371,6 +1575,65 @@ const makePatternKit = () => {
       );
     },
 
+    // Compress to a pair of bindings arrays, one for the keys
+    // and a matching one for the values.
+    compress: (
+      specimen,
+      [keyPatt, valuePatt, limits = undefined],
+      compress,
+    ) => {
+      const { numMapEntriesLimit } = limit(limits);
+      if (
+        isKind(specimen, 'copyMap') &&
+        /** @type {Array} */ (specimen.payload.keys).length <=
+          numMapEntriesLimit
+      ) {
+        const compressedKeys = arrayCompressMatchPattern(
+          specimen.payload.keys,
+          keyPatt,
+          compress,
+        );
+        if (compressedKeys) {
+          const compressedValues = arrayCompressMatchPattern(
+            specimen.payload.values,
+            valuePatt,
+            compress,
+          );
+          if (compressedValues) {
+            return harden({
+              compressed: [compressedKeys, compressedValues],
+            });
+          }
+        }
+      }
+      return undefined;
+    },
+
+    decompress: (
+      compressed,
+      [keyPatt, valuePatt, _limits = undefined],
+      decompress,
+    ) => {
+      (Array.isArray(compressed) && compressed.length === 2) ||
+        Fail`Compressed map should be a pair of compressed keys and compressed values ${compressed}`;
+      const [compressedKeys, compressedvalues] = compressed;
+      return makeTagged(
+        'copyMap',
+        harden({
+          keys: arrayDecompressMatchPattern(
+            compressedKeys,
+            keyPatt,
+            decompress,
+          ),
+          values: arrayDecompressMatchPattern(
+            compressedvalues,
+            valuePatt,
+            decompress,
+          ),
+        }),
+      );
+    },
+
     checkIsWellFormed: (payload, check) =>
       checkIsWellFormedWithLimit(
         payload,
@@ -1418,7 +1681,7 @@ const makePatternKit = () => {
 
   /** @type {MatchHelper} */
   const matchSplitArrayHelper = harden({
-    tag: `match:splitArray`,
+    tag: `match:splitArray:1`,
 
     checkMatches: (
       specimen,
@@ -1455,6 +1718,70 @@ const makePatternKit = () => {
       );
     },
 
+    compress: (
+      specimen,
+      [requiredPatt, optionalPatt = [], restPatt = MM.any()],
+      compress,
+    ) => {
+      if (!checkKind(specimen, 'copyArray', identChecker)) {
+        return undefined;
+      }
+      const { requiredSpecimen, optionalSpecimen, restSpecimen } =
+        splitArrayParts(specimen, requiredPatt, optionalPatt);
+      const partialPatt = adaptArrayPattern(
+        optionalPatt,
+        optionalSpecimen.length,
+      );
+      const compressedRequired = compress(requiredSpecimen, requiredPatt);
+      if (!compressedRequired) {
+        return undefined;
+      }
+      const compressedPartial = [];
+      for (const [i, p] of entries(partialPatt)) {
+        const compressedField = compress(optionalSpecimen[i], p);
+        if (!compressedField) {
+          // imperative loop so can escape early
+          return undefined;
+        }
+        compressedPartial.push(compressedField.compressed[0]);
+      }
+      const compressedRest = compress(restSpecimen, restPatt);
+      if (!compressedRest) {
+        return undefined;
+      }
+      return harden({
+        compressed: [
+          compressedRequired.compressed,
+          compressedPartial,
+          compressedRest.compressed,
+        ],
+      });
+    },
+
+    decompress: (
+      compressed,
+      [requiredPatt, optionalPatt = [], restPatt = MM.any()],
+      decompress,
+    ) => {
+      (Array.isArray(compressed) && compressed.length === 3) ||
+        Fail`splitArray compression must be a triple ${compressed}`;
+      const [compressRequired, compressPartial, compressedRest] = compressed;
+      const partialPatt = adaptArrayPattern(
+        optionalPatt,
+        compressPartial.length,
+      );
+      const requiredParts = decompress(compressRequired, requiredPatt);
+      // const optionalParts = decompress(compressPartial, partialPatt);
+      const optionalParts = [];
+      for (const [i, p] of entries(partialPatt)) {
+        // imperative loop just for similarity to compression code
+        const optionalField = decompress(harden([compressPartial[i]]), p);
+        optionalParts.push(optionalField);
+      }
+      const restParts = decompress(compressedRest, restPatt);
+      return harden([...requiredParts, ...optionalParts, ...restParts]);
+    },
+
     /**
      * @param {Array} splitArray
      * @param {Checker} check
@@ -1539,7 +1866,7 @@ const makePatternKit = () => {
 
   /** @type {MatchHelper} */
   const matchSplitRecordHelper = harden({
-    tag: `match:splitRecord`,
+    tag: `match:splitRecord:1`,
 
     checkMatches: (
       specimen,
@@ -1568,6 +1895,87 @@ const makePatternKit = () => {
       );
     },
 
+    compress: (
+      specimen,
+      [requiredPatt, optionalPatt = {}, restPatt = MM.any()],
+      compress,
+    ) => {
+      if (!checkKind(specimen, 'copyRecord', identChecker)) {
+        return undefined;
+      }
+      const { requiredSpecimen, optionalSpecimen, restSpecimen } =
+        splitRecordParts(specimen, requiredPatt, optionalPatt);
+      const partialPatt = adaptRecordPattern(optionalPatt);
+
+      const compressedRequired = compress(requiredSpecimen, requiredPatt);
+      if (!compressedRequired) {
+        return undefined;
+      }
+      const optionalNames = recordNames(partialPatt);
+      const compressedPartial = [];
+      for (const name of optionalNames) {
+        if (hasOwn(optionalSpecimen, name)) {
+          const compressedField = compress(
+            optionalSpecimen[name],
+            partialPatt[name],
+          );
+          if (!compressedField) {
+            return undefined;
+          }
+          compressedPartial.push(compressedField.compressed[0]);
+        } else {
+          compressedPartial.push(null);
+        }
+      }
+      const compressedRest = compress(restSpecimen, restPatt);
+      if (!compressedRest) {
+        return undefined;
+      }
+      return harden({
+        compressed: [
+          compressedRequired.compressed,
+          compressedPartial,
+          compressedRest.compressed,
+        ],
+      });
+    },
+
+    decompress: (
+      compressed,
+      [requiredPatt, optionalPatt = {}, restPatt = MM.any()],
+      decompress,
+    ) => {
+      (Array.isArray(compressed) && compressed.length === 3) ||
+        Fail`splitRecord compression must be a triple ${compressed}`;
+      const [compressedRequired, compressedPartial, compressedRest] =
+        compressed;
+      const partialPatt = adaptRecordPattern(optionalPatt);
+      const requiredEntries = entries(
+        decompress(compressedRequired, requiredPatt),
+      );
+      const optionalNames = recordNames(partialPatt);
+      compressedPartial.length === optionalNames.length ||
+        Fail`compression or patterns must preserve cardinality: ${compressedPartial}`;
+      /** @type {[string, Passable][]} */
+      const optionalEntries = [];
+      for (const [i, name] of entries(optionalNames)) {
+        const p = partialPatt[name];
+        const c = compressedPartial[i];
+        if (c !== null) {
+          const u = decompress(harden([c]), p);
+          optionalEntries.push([name, u]);
+        }
+      }
+      const restEntries = entries(decompress(compressedRest, restPatt));
+
+      const allEntries = [
+        ...requiredEntries,
+        ...optionalEntries,
+        ...restEntries,
+      ];
+      return fromUniqueEntries(allEntries);
+    },
+
     /**
      * @param {Array} splitArray
      * @param {Checker} check
@@ -1642,13 +2050,21 @@ const makePatternKit = () => {
     const helpersByMatchTag = {};
 
     for (const helper of helpers) {
-      const { tag } = helper;
+      const { tag, compress, decompress, ...rest } = helper;
       if (!matchHelperTagRE.test(tag)) {
         throw Fail`malformed matcher tag ${q(tag)}`;
       }
       const subTag = getMatchSubTag(tag);
-      subTag === undefined ||
-        Fail`Should not be any subtags before compression ${q(tag)}`;
+      if (subTag === undefined) {
+        (compress === undefined && decompress === undefined) ||
+          Fail`internal: compressing helper must have compression version ${q(
+            tag,
+          )}`;
+      } else {
+        (typeof compress === 'function' && typeof decompress === 'function') ||
+          Fail`internal: expected compression methods ${q(tag)})`;
+        helpersByMatchTag[subTag] = { tag: subTag, ...rest };
+      }
       helpersByMatchTag[tag] = helper;
     }
     return harden(helpersByMatchTag);
diff --git a/packages/patterns/src/patterns/types.js b/packages/patterns/src/patterns/types.js
index 77e835afd5..fdc6037633 100644
--- a/packages/patterns/src/patterns/types.js
+++ b/packages/patterns/src/patterns/types.js
@@ -4,7 +4,7 @@ export {};
 
 /**
  * @import {Passable, Checker} from '@endo/pass-style'
- * @import {MatcherNamespace, Pattern, GetRankCover, Kind} from '../types.js'
+ * @import {MatcherNamespace, Pattern, GetRankCover, Compress, Decompress, CompressedRecord, Kind} from '../types.js'
  */
 
 /**
@@ -28,6 +28,27 @@ export {};
  * Assuming validity of `matcherPayload` as the payload of a Matcher corresponding
  * with this MatchHelper, reports whether `specimen` is matched by that Matcher.
  *
+ * @property {(specimen: Passable,
+ *             matcherPayload: Passable,
+ *             compress: Compress
+ * ) => (CompressedRecord | undefined)} [compress]
+ * Assuming a valid Matcher of this type with `matcherPayload` as its
+ * payload, if this specimen matches this matcher, then return a
+ * CompressedRecord that represents this specimen,
+ * perhaps more compactly, given the knowledge that it matches this matcher.
+ * If the specimen does not match the matcher, return undefined.
+ * If this matcher has a `compress` method, then it must have a matching
+ * `decompress` method.
+ *
+ * @property {(compressed: Passable,
+ *             matcherPayload: Passable,
+ *             decompress: Decompress
+ * ) => Passable} [decompress]
+ * If `compressed` is the result of a successful `compress` with this matcher,
+ * then `decompress` must return a Passable equivalent to the original specimen.
+ * If this matcher has an `decompress` method, then it must have a matching
+ * `compress` method.
+ *
  * @property {GetRankCover} getRankCover
  * Assumes this is the payload of a CopyTagged with the corresponding
  * matchTag. Return a RankCover to bound from below and above,
diff --git a/packages/patterns/src/types.js b/packages/patterns/src/types.js
index cbb4b6fa19..c84a0a5128 100644
--- a/packages/patterns/src/types.js
+++ b/packages/patterns/src/types.js
@@ -236,6 +236,41 @@ export {};
  * that the @endo/patterns level associates with that kind.
  */
 
+/**
+ * @typedef {object} CompressedRecord
+ * @property {Passable} compressed
+ */
+
+/**
+ * @callback Compress
+ * @param {Passable} specimen
+ * @param {Pattern} pattern
+ * @returns {CompressedRecord | undefined}
+ */
+
+/**
+ * @callback MustCompress
+ * @param {Passable} specimen
+ * @param {Pattern} pattern
+ * @param {string|number} [label]
+ * @returns {Passable}
+ */
+
+/**
+ * @callback Decompress
+ * @param {Passable} compressed
+ * @param {Pattern} pattern
+ * @returns {Passable}
+ */
+
+/**
+ * @callback MustDecompress
+ * @param {Passable} compressed
+ * @param {Pattern} pattern
+ * @param {string|number} [label]
+ * @returns {Passable}
+ */
+
 /**
  * @typedef {object} PatternMatchers
  *
diff --git a/packages/patterns/test/test-compress.js b/packages/patterns/test/test-compress.js
new file mode 100644
index 0000000000..d745428f8c
--- /dev/null
+++ b/packages/patterns/test/test-compress.js
@@ -0,0 +1,273 @@
+// @ts-nocheck So many errors that the suppressions hamper readability.
+// TODO fix and then turn at-ts-check back on
+import test from '@endo/ses-ava/prepare-endo.js';
+
+import { Far, makeTagged, makeMarshal } from '@endo/marshal';
+import {
+  makeCopyBagFromElements,
+  makeCopyMap,
+  makeCopySet,
+} from '../src/keys/checkKey.js';
+import { mustCompress, mustDecompress } from '../src/patterns/compress.js';
+import { M } from '../src/patterns/patternMatchers.js';
+
+const runTests = testTriple => {
+  const brand = Far('simoleans', {});
+  const moolaBrand = Far('moola', {});
+  const timer = Far('timer', {});
+
+  testTriple({ brand, value: 37n }, M.any(), { brand, value: 37n });
+  testTriple({ brand, value: 37n }, { brand, value: M.bigint() }, [37n]);
+  testTriple(
+    { brand, value: 37n },
+    { brand: M.remotable(), value: M.bigint() },
+    [37n, brand],
+  );
+  testTriple(
+    { brand, value: 37n },
+    { brand: M.bigint(), value: M.bigint() },
+    undefined,
+    'test mustCompress: brand: remotable "[Alleged: simoleans]" - Must be a bigint',
+  );
+  testTriple({ brand, value: 37n }, M.recordOf(M.string(), M.scalar()), {
+    brand,
+    value: 37n,
+  });
+  testTriple(
+    [{ foo: 'a' }, { foo: 'b' }, { foo: 'c' }],
+    M.arrayOf(harden({ foo: M.string() })),
+    [[['a'], ['b'], ['c']]],
+  );
+  testTriple(
+    [{ foo: 'a' }, { foo: 'b' }, { foo: 'c' }],
+    // Test that without the compression version tag, there is no
+    // non -default compression or decompression
+    makeTagged('match:arrayOf', harden([{ foo: M.string() }])),
+    [{ foo: 'a' }, { foo: 'b' }, { foo: 'c' }],
+  );
+  testTriple(
+    makeCopySet([{ foo: 'a' }, { foo: 'b' }, { foo: 'c' }]),
+    M.setOf(harden({ foo: M.string() })),
+    [[['c'], ['b'], ['a']]],
+  );
+  testTriple(
+    makeCopyBagFromElements([{ foo: 'a' }, { foo: 'a' }, { foo: 'c' }]),
+    M.bagOf(harden({ foo: M.string() })),
+    [
+      [
+        ['c', 1n],
+        ['a', 2n],
+      ],
+    ],
+  );
+  testTriple(
+    makeCopyBagFromElements([{ foo: 'a' }, { foo: 'a' }, { foo: 'c' }]),
+    M.bagOf(harden({ foo: M.string() }), 1n),
+    undefined,
+    'test mustCompress: bag counts[1]: "[2n]" - Must be: "[1n]"',
+  );
+  testTriple(
+    makeCopyBagFromElements([{ foo: 'a' }, { foo: 'b' }, { foo: 'c' }]),
+    M.bagOf(harden({ foo: M.string() }), 1n),
+    [[['c'], ['b'], ['a']]],
+  );
+  testTriple(
+    makeCopyMap([
+      [{ foo: 'a' }, { bar: 1 }],
+      [{ foo: 'b' }, { bar: 2 }],
+      [{ foo: 'c' }, { bar: 3 }],
+    ]),
+    M.mapOf(harden({ foo: M.string() }), harden({ bar: M.number() })),
+    [
+      [
+        [['c'], ['b'], ['a']],
+        [[3], [2], [1]],
+      ],
+    ],
+  );
+  testTriple(
+    makeCopyMap([
+      [{ foo: 'c' }, { bar: 3 }],
+      [{ foo: 'b' }, { bar: 2 }],
+      [{ foo: 'a' }, { bar: 1 }],
+    ]),
+    // TODO Add a test case where the keys are in the same rankOrder but not
+    // the same order.
+    makeCopyMap([
+      [{ foo: 'c' }, M.any()],
+      // @ts-expect-error The array need not be generic
+      [{ foo: 'b' }, { bar: M.number() }],
+      [{ foo: 'a' }, { bar: 1 }],
+    ]),
+    [{ bar: 3 }, 2],
+  );
+  testTriple(
+    {
+      want: { Winnings: { brand: moolaBrand, value: ['x', 'y'] } },
+      give: { Bid: { brand, value: 37n } },
+      exit: { afterDeadline: { deadline: 11n, timer } },
+    },
+    {
+      want: { Winnings: { brand: moolaBrand, value: M.array() } },
+      give: { Bid: { brand, value: M.nat() } },
+      exit: { afterDeadline: { deadline: M.gte(10n), timer } },
+    },
+    [['x', 'y'], 37n, 11n],
+  );
+  testTriple(
+    {
+      want: {
+        Winnings: {
+          brand: moolaBrand,
+          value: makeCopyBagFromElements([
+            { foo: 'a' },
+            { foo: 'b' },
+            { foo: 'c' },
+          ]),
+        },
+      },
+      give: { Bid: { brand, value: 37n } },
+      exit: { afterDeadline: { deadline: 11n, timer } },
+    },
+    {
+      want: {
+        Winnings: {
+          brand: moolaBrand,
+          value: M.bagOf(harden({ foo: M.string() }), 1n),
+        },
+      },
+      give: { Bid: { brand, value: M.nat() } },
+      exit: { afterDeadline: { deadline: M.gte(10n), timer } },
+    },
+    [[['c'], ['b'], ['a']], 37n, 11n],
+  );
+  testTriple(
+    'orange',
+    M.or('red', 'orange', 'yellow', 'green', 'blue', 'indigo', 'violet'),
+    [[1, []]],
+  );
+  testTriple(
+    { x: 3, y: 5 },
+    M.or(harden({ x: M.number(), y: M.number() }), M.bigint(), M.record()),
+    [[0, [5, 3]]],
+  );
+  testTriple(
+    [5n],
+    M.or(harden({ x: M.number(), y: M.number() }), [M.bigint()], M.record()),
+    [[1, [5n]]],
+  );
+  testTriple(
+    { x: 3, y: 5, z: 9 },
+    M.or(harden({ x: M.number(), y: M.number() }), M.bigint(), M.record()),
+    [[2, { x: 3, y: 5, z: 9 }]],
+  );
+  testTriple(
+    {
+      brand,
+      value: [{ bar: 2 }, { bar: 1 }],
+    },
+    {
+      brand,
+      value: M.arrayOf(M.and(M.key(), { bar: M.number() })),
+    },
+    [[[[2]], [[1]]]],
+  );
+  testTriple(
+    ['a', 'b', 'c', 'd', 'e'],
+    M.splitArray(['a', M.string()], [M.any()], M.any()),
+    [[['b'], [[1, 'c']], ['d', 'e']]],
+  );
+  testTriple(
+    ['a', 'b', undefined, 'd'],
+    M.splitArray(['a', M.string()], ['c', 'd', 'e'], M.any()),
+    [
+      [
+        ['b'],
+        [
+          [0, []],
+          [1, []],
+        ],
+        [],
+      ],
+    ],
+  );
+  testTriple(
+    { a: 1, b: 2, c: undefined, d: 4, e: 5 },
+    M.splitRecord({ a: 1, b: M.number() }, { c: M.any(), d: 4, f: 6 }, M.any()),
+    [[[2], [null, [1, []], [0, []]], { e: 5 }]],
+  );
+  testTriple(
+    makeTagged('foo', { a: 1, b: 2 }),
+    M.tagged('foo', harden({ a: 1, b: M.number() })),
+    [[[], [2]]],
+  );
+};
+
+test('compression', t => {
+  const testCompress = (specimen, pattern, compressed, message = undefined) => {
+    if (!message) {
+      t.deepEqual(
+        mustCompress(harden(specimen), harden(pattern)),
+        harden(compressed),
+      );
+    }
+  };
+  runTests(testCompress);
+});
+
+test('test mustCompress', t => {
+  const testCompress = (specimen, pattern, compressed, message = undefined) => {
+    if (message === undefined) {
+      t.deepEqual(
+        mustCompress(harden(specimen), harden(pattern), 'test mustCompress'),
+        harden(compressed),
+      );
+    } else {
+      t.throws(
+        () =>
+          mustCompress(harden(specimen), harden(pattern), 'test mustCompress'),
+        { message },
+      );
+    }
+  };
+  runTests(testCompress);
+});
+
+test('decompression', t => {
+  const testDecompress = (
+    specimen,
+    pattern,
+    compressed,
+    message = undefined,
+  ) => {
+    if (message === undefined) {
+      t.deepEqual(
+        mustDecompress(harden(compressed), harden(pattern)),
+        harden(specimen),
+      );
+    }
+  };
+  runTests(testDecompress);
+});
+
+test('demo compression ratio', t => {
+  const { toCapData } = makeMarshal(() => 's', undefined, {
+    serializeBodyFormat: 'smallcaps',
+  });
+
+  const testCompress = (specimen, pattern, compressed, message = undefined) => {
+    harden(specimen);
+    harden(pattern);
+    harden(compressed);
+    if (message === undefined) {
+      const { body: big } = toCapData(specimen);
+      const { body: small } = toCapData(compressed);
+      const ratio = small.length / big.length;
+      console.log('\n', big, '\n', small, '\n', ratio);
+      const { body: patt } = toCapData(pattern);
+      console.log('Pattern: ', patt);
+      t.assert(ratio <= 2.0);
+    }
+  };
+  runTests(testCompress);
+});