diff --git a/contracts/contracts/FallbackExpander.sol b/contracts/contracts/FallbackExpander.sol
index 3fd49e7e..97edb022 100644
--- a/contracts/contracts/FallbackExpander.sol
+++ b/contracts/contracts/FallbackExpander.sol
@@ -3,6 +3,7 @@ pragma solidity >=0.7.0 <0.9.0;
 pragma abicoder v2;
 
 import "./lib/VLQ.sol";
+import "./lib/PseudoFloat.sol";
 import "./interfaces/IExpander.sol";
 import "./interfaces/IWallet.sol";
 
@@ -22,16 +23,16 @@ import "./interfaces/IWallet.sol";
  * 24f1fc8a1f7256dc2914e524966309df2226fd329373aaaae1881bf5cd0c62f4 // BLS key
  *
  * 00 // nonce: 0
- * 868d20 // gas: 100,000
+ * 3100 // gas: 100,000
  * 02 // two actions
  *
  * // Action 1
- * 95ecd98ed5f38000 // ethValue: 12300000000000000 (0.0123 ETH)
+ * 7b0f // ethValue: 12300000000000000 (0.0123 ETH)
  * 70997970c51812dc3a010c7d01b50e0d17dc79c8 // contractAddress
  * 00 // encodedFunction: (empty)
  *
  * // Action 2
- * 82dd9fbdf38000 // ethValue: 12000000000000 (0.000012 ETH)
+ * 6c01 // ethValue: 12000000000000 (0.000012 ETH)
  * 4bd2e4e99b50a2a9e6b9dabfa3c8dcd1f885f008 // contractAddress (AggUtils)
  * 04 // 4 bytes for encodedFunction
  * 1dfea6a0 // sendEthToTxOrigin
@@ -39,8 +40,8 @@ import "./interfaces/IWallet.sol";
  * The proposal doc for the new expander lists the same example ("Example of an
  * Expanded User Operation" https://hackmd.io/0q7H3Ad0Su-I4RWWK8wQPA) using the
  * solidity ABI, which uses 608 bytes. Here we've encoded the same thing (plus
- * gas) in 194 bytes, which is (about) 70% smaller. (If you account for the
- * zero-byte discount, the saving is still over 30%.)
+ * gas) in 182 bytes, which is 70% smaller. (If you account for the zero-byte
+ * discount, the saving is still over 30%.)
  */
 contract FallbackExpander is IExpander {
     function expand(bytes calldata stream) external pure returns (
@@ -49,30 +50,30 @@ contract FallbackExpander is IExpander {
         uint256 bytesRead
     ) {
         uint256 originalStreamLen = stream.length;
-        uint256 vlqValue;
+        uint256 decodedValue;
 
         senderPublicKey = abi.decode(stream[:128], (uint256[4]));
         stream = stream[128:];
 
-        (vlqValue, stream) = VLQ.decode(stream);
-        operation.nonce = vlqValue;
+        (decodedValue, stream) = VLQ.decode(stream);
+        operation.nonce = decodedValue;
 
-        (vlqValue, stream) = VLQ.decode(stream);
-        operation.gas = vlqValue;
+        (decodedValue, stream) = PseudoFloat.decode(stream);
+        operation.gas = decodedValue;
 
-        (vlqValue, stream) = VLQ.decode(stream);
-        operation.actions = new IWallet.ActionData[](vlqValue);
+        (decodedValue, stream) = VLQ.decode(stream);
+        operation.actions = new IWallet.ActionData[](decodedValue);
 
         for (uint256 i = 0; i < operation.actions.length; i++) {
             uint256 ethValue;
-            (ethValue, stream) = VLQ.decode(stream);
+            (ethValue, stream) = PseudoFloat.decode(stream);
 
             address contractAddress = address(bytes20(stream[:20]));
             stream = stream[20:];
 
-            (vlqValue, stream) = VLQ.decode(stream);
-            bytes memory encodedFunction = stream[:vlqValue];
-            stream = stream[vlqValue:];
+            (decodedValue, stream) = VLQ.decode(stream);
+            bytes memory encodedFunction = stream[:decodedValue];
+            stream = stream[decodedValue:];
 
             operation.actions[i] = IWallet.ActionData({
                 ethValue: ethValue,
diff --git a/contracts/contracts/lib/PseudoFloat.sol b/contracts/contracts/lib/PseudoFloat.sol
new file mode 100644
index 00000000..f278daca
--- /dev/null
+++ b/contracts/contracts/lib/PseudoFloat.sol
@@ -0,0 +1,117 @@
+//SPDX-License-Identifier: Unlicense
+pragma solidity >=0.7.0 <0.9.0;
+pragma abicoder v2;
+
+import "./VLQ.sol";
+
+/**
+ * Like a float, but technically for integers. Also base 10.
+ *
+ * The pseudo-float is an encoding that can represent any uint256 value but
+ * efficiently represents values with a small number of significant figures
+ * (just 2 bytes for 3 significant figures).
+ *
+ * Zero is a special case, it's just 0x00.
+ *
+ * Otherwise, start with the value in scientific notation:
+ *
+ *     1.23 * 10^16 (e.g. 0.0123 ETH)
+ *
+ * Make the mantissa (1.23) a whole number by adjusting the exponent:
+ *
+ *     123 * 10^14
+ *
+ * We add 1 to the exponent and encode it in 5 bits:
+ *
+ *     01111 (=15)
+ *
+ *     Note: The maximum value we can encode here is 31 (11111). This means the
+ *     maximum exponent is 30. Adjust the left side of the previous equation if
+ *     needed.
+ *
+ * Encode the left side in binary:
+ *
+ *     1111011 (=123)
+ *
+ * Our first byte is the 5-bit exponent followed by the three lowest bits of the
+ * mantissa:
+ * 
+ *     01111011
+ *     ^^^^^-------- 15 => exponent is 14
+ *          ^^^----- lowest 3 bits of the mantissa
+ *
+ * Encode the remaining bits of the mantissa as a VLQ:
+ *
+ *     00001111
+ *     ^------------ special VLQ bit, zero indicates this is the last byte
+ *      ^^^^^^^----- bits to use, put them together with 011 above to get
+ *                   0001111011, which is 123.
+ *
+ * Putting it together is two bytes:
+ *
+ *     0x7b0f
+ *
+ * Example 2:
+ *
+ *     0.883887085 ETH uses 5 bytes: 0x55b4d7c27d
+ *     883887085 * 10^9
+ *     For exponent 9 we encode 10 as 5 bits: 01010
+ *     883887085 is 110100101011110000101111101(101)
+ *
+ *     01010101 10110100 11010111 11000010 01111101
+ *     ^^^^^------------------------------------------- 10 => exponent is 9
+ *          ^^^---------------------------------------- lowest 3 bits
+ *               ^^^^^^^--^^^^^^^--^^^^^^^--^^^^^^^     higher bits
+ *              ^--------^--------^-------------------- 1 => not the last byte
+ *                                         ^----------- 0 => the last byte
+ *
+ * Note that the *encode* process is described above for explanatory purposes.
+ * On-chain we need to *decode* to recover the value from the encoded binary
+ * instead.
+ */
+library PseudoFloat {
+    function decode(
+        bytes calldata stream
+    ) internal pure returns (uint256, bytes calldata) {
+        uint8 firstByte = uint8(stream[0]);
+
+        if (firstByte == 0) {
+            return (0, stream[1:]);
+        }
+
+        uint8 exponent = ((firstByte & 0xf8) >> 3) - 1;
+
+        uint256 value;
+        (value, stream) = VLQ.decode(stream[1:]);
+
+        value <<= 3;
+        value += firstByte & 0x07;
+
+        // TODO (merge-ok): Exponentiation by squaring might be better here.
+        // Counterpoints:
+        // - The gas used is pretty low anyway
+        // - For these low exponents (typically ~15), the benefit is unclear
+        for (uint256 i = 0; i < exponent; i++) {
+            value *= 10;
+        }
+
+        return (value, stream);
+    }
+
+    /**
+     * Same as decode, but public.
+     * 
+     * This is here because when a library function that is not internal
+     * requires linking when used in other contracts. This avoids including a
+     * copy of that function in the contract but it's complexity that we don't
+     * want right now.
+     * 
+     * What we do want though, is a public version so that we can call it
+     * statically for testing.
+     */
+    function decodePublic(
+        bytes calldata stream
+    ) public pure returns (uint256, bytes calldata) {
+        return decode(stream);
+    }
+}
diff --git a/contracts/contracts/lib/VLQ.sol b/contracts/contracts/lib/VLQ.sol
index 436cd8bb..de434147 100644
--- a/contracts/contracts/lib/VLQ.sol
+++ b/contracts/contracts/lib/VLQ.sol
@@ -1,4 +1,4 @@
-//SPDX-License-Identifier: MIT
+//SPDX-License-Identifier: Unlicense
 pragma solidity >=0.7.0 <0.9.0;
 pragma abicoder v2;
 
diff --git a/contracts/shared/helpers/bundleCompression.ts b/contracts/shared/helpers/bundleCompression.ts
index aeb6acc5..a4166838 100644
--- a/contracts/shared/helpers/bundleCompression.ts
+++ b/contracts/shared/helpers/bundleCompression.ts
@@ -26,12 +26,12 @@ export function compressAsFallback(
   );
 
   result.push(encodeVLQ(operation.nonce));
-  result.push(encodeVLQ(operation.gas));
+  result.push(encodePseudoFloat(operation.gas));
 
   result.push(encodeVLQ(operation.actions.length));
 
   for (const action of operation.actions) {
-    result.push(encodeVLQ(action.ethValue));
+    result.push(encodePseudoFloat(action.ethValue));
     result.push(action.contractAddress);
 
     const fnHex = ethers.utils.hexlify(action.encodedFunction);
@@ -56,7 +56,7 @@ function remove0x(hexString: string) {
   return hexString.slice(2);
 }
 
-function encodeVLQ(x: BigNumberish) {
+export function encodeVLQ(x: BigNumberish) {
   x = BigNumber.from(x);
 
   const segments: number[] = [];
@@ -83,3 +83,27 @@ function encodeVLQ(x: BigNumberish) {
 
   return result;
 }
+
+export function encodePseudoFloat(x: BigNumberish) {
+  x = BigNumber.from(x);
+
+  if (x.eq(0)) {
+    return "0x00";
+  }
+
+  let exponent = 0;
+
+  while (x.mod(10).eq(0) && exponent < 30) {
+    x = x.div(10);
+    exponent++;
+  }
+
+  const exponentBits = (exponent + 1).toString(2).padStart(5, "0");
+  const lowest3Bits = x.mod(8).toNumber().toString(2).padStart(3, "0");
+
+  const firstByte = parseInt(`${exponentBits}${lowest3Bits}`, 2)
+    .toString(16)
+    .padStart(2, "0");
+
+  return hexJoin([`0x${firstByte}`, encodeVLQ(x.div(8))]);
+}
diff --git a/contracts/test/pseudoFloat-test.ts b/contracts/test/pseudoFloat-test.ts
new file mode 100644
index 00000000..0288ca3a
--- /dev/null
+++ b/contracts/test/pseudoFloat-test.ts
@@ -0,0 +1,357 @@
+/* eslint-disable camelcase */
+
+import { expect } from "chai";
+import { BigNumber } from "ethers";
+import { RLP } from "ethers/lib/utils";
+import { ethers } from "hardhat";
+import { encodePseudoFloat } from "../shared/helpers/bundleCompression";
+import { PseudoFloat, PseudoFloat__factory } from "../typechain-types";
+
+describe("PseudoFloat", function () {
+  let pseudoFloat: PseudoFloat;
+
+  this.beforeAll(async () => {
+    const [eoa] = await ethers.getSigners();
+    const factory = new PseudoFloat__factory(eoa);
+    pseudoFloat = await factory.deploy();
+  });
+
+  it("0x00 -> 0", async () => {
+    const [value, stream] = await pseudoFloat.decodePublic("0x00");
+    expect(value).to.eq(0);
+    expect(stream).to.eq("0x");
+  });
+
+  it("0x7b0f -> 0.0123 ETH", async () => {
+    const [value, stream] = await pseudoFloat.decodePublic("0x7b0f");
+    expect(ethers.utils.formatEther(value)).to.eq("0.0123");
+    expect(stream).to.eq("0x");
+  });
+
+  it("0x55b4d7c27d -> 0.883887085 ETH", async () => {
+    const [value, stream] = await pseudoFloat.decodePublic("0x55b4d7c27d");
+    expect(ethers.utils.formatEther(value)).to.eq("0.883887085");
+    expect(stream).to.eq("0x");
+  });
+
+  it("Test tx.values from 20 blocks", async () => {
+    // The non-zero tx.value amounts of transactions in mainnet blocks 16472849
+    // to 16472868, excluding zeros.
+
+    const rlpEncodedTxValueSamples = [
+      "0xf925d6870a1d40bbff073682b0068704229bc64a50dd88010e0198eaee000087c9",
+      "94bab88e400088120a871cc002000088013e2d45b49a680088021d84798d7aa80087",
+      "6bacaa5051dc0088019ffc683f1410008603b3cb0fa4bc8603be095cbdca87470de4",
+      "df8200008801aa535d3d0c00008751007aace100008740cd2ef0b40000880123cff5",
+      "23f50c0087eafe86ecab100088136bbd135793c00087a7b02661660000876a94d74f",
+      "4300008801936ae92fd50fd087470de4df8200008758d15e1762800088063eb89da4",
+      "ed000087670758aa7c800087ae153d89fe80008707d0e36a81800088011c37937e08",
+      "00008724568d2810178f875644b7c0a9f01087ae153d89fe800087dc44abe8130000",
+      "875543df729c0000870590c4b1d13040877fe5cf2bea000087557c95fe3d0a9b8801",
+      "86cc6acd4b00008719396991e7c00088013bd51fe73151008798d6758217bcc887e5",
+      "40d692fd6800890c77e4256863d8000087470de4df82000087470de4df82000087df",
+      "d22a8cd9800087982cd1740208088715d141218fbf558803782dace9d90000880429",
+      "d069189e000088021f567b515e800088013fbe85edc900008801621a7b4e1ab16087",
+      "6a00d5c0dadf438331dc65880429d069189e0000833558fd8703ea0048a75b1282b5",
+      "0488018de76816d80000880426dfaad05e6c0087d08b56c850c00087e35fa931a000",
+      "008751ca0cee4cec00880214e8348c4f000088016345785d8a0000870a15e3bec7dd",
+      "8488154b96e763c997c0877fe5cf2bea00008803782dace9d9000087b1a2bc2ec500",
+      "008904e0fbf7c4136d0000880199ec80018328008904b26dde93c5fdd0ed88019d3c",
+      "6507b274008801cc6e836ae4000088019174e6bb9e8000882f53f7957d3a195a8707",
+      "d0e36a81800087f8b0a10e470000870100ce7d8a443488136dcc951d8c000087ba2b",
+      "4a048462de87180887928e719587b5303ad38b800088016345785d8a000087180887",
+      "928e7195871550f7dca70000873a84f40db5e00c8802c68af0bb140000872386f26f",
+      "c100008805f916850754000088044739bb8841ee988704a8688647665787b0f876d0",
+      "fd156d83410d9e8801aa535d3d0c00008802c68af0bb1400008345ab158603af8205",
+      "f5158801cdda4faccd00008603e82a0d90fa82a7048205048802c68af0bb14000087",
+      "470de4df820000870678e465868b108706935b24557b108751a7d040a02f58880184",
+      "183c20307ec48729297ccac92400880646e08f1ab9228487234e47c27fe5bc880ea6",
+      "2d68d0bddfb08801063112a248200087552707f2bcb91d872386f26fc10000871b09",
+      "4132bda000875967f4067306458803bf3b91c95b000088011fc51222ce800087a809",
+      "b0e62f4c8d8830927f74c9de000087132f4579c98000876a94d74f430000871c6bf5",
+      "263400008707d0e36a818000871b5b1bf4c540008735cfec17b87b708801aa535d3d",
+      "0c0000880713e24c4373000087d529ae9e86000087a200f559c20000880429d06918",
+      "9e0000881c01604ee4bd0000870942d79f01f7878711c37937e0800087b1a2bc2ec5",
+      "000087f8b0a10e47000088063eb89da4ed000087b5303ad38b8000886e794fd07f2d",
+      "291a8802b300b830d04000871ee491510e2a1d873ff2e795f50000881bc16d674ec8",
+      "00008829a2241af62c000088016345785d8a000088019c09029f9123808705d7b6d5",
+      "6b491d87077de673ecbb9487868bbe764dc12688016345785d8a000088027f7d0bdb",
+      "92000088013fbe85edc900008701579637a959b888016345785d8a0000878ecbc7a5",
+      "01eb5088035834391ede800087e526688403400087e526688403400087e526688403",
+      "400087e63741b5720000872846082d2c80008740cd2ef0b400008803782dace9d900",
+      "008807aa9455ace3104088013b1ec6ae987aa88369da24836dea148802c68af0bb14",
+      "0000870a5caa60bd3e9687b1a2bc2ec5000088023241283b9db06087b1a2bc2ec500",
+      "0087b1a2bc2ec5000087b1a2bc2ec50000865af3107a400087b1a2bc2ec500008801",
+      "2dfb0cb5e88000880d7a7cba64ea99b08801efd8ca11c9f7e88705fdf459ee094887",
+      "b1a2bc2ec50000870360a817c9b800870360a817c9b8008801e2839ba83045cf87c1",
+      "09d97031780087d4601fcaf9a4b088018e072b7720688b87470de4df82000087cc47",
+      "f20295c0008780c7eddff0afbe876a94d74f4300008801cdda4faccd00008815f96b",
+      "66219001d0880194c8dd0ce36c1c8802d84e69f2f4800087d4cea44594d80088077e",
+      "772392b6000087025b651454c4be8707d0e36a8180008802fbd55c62b58000880de0",
+      "b6b3a76400008731bced02db000087f8b0a10e4700008810e44ac2d7b5c000872386",
+      "f26fc1000088019502656065000087a59ee710c7a34b87138a388a43e338890107ad",
+      "8f556c6c00008751b660cdd58000873da194b0e6af8f8801ddd709924a4000873c65",
+      "68f12e80008751b660cdd5800087f8b0a10e470000876a94d74f43000087354a6ba7",
+      "a180008712795f58d50000877c58508723800087470de4df82000088031126543f5c",
+      "800088016345785d8a000087f0631f499afd0a830b8a7a880429d069189e0000830c",
+      "460d870a200f559c20008704907ac3125b158802c68af0bb140000871b314439129a",
+      "988758d15e1762800087046aacba569c0087121e6c485ac000881a5a5a92c3dda763",
+      "88016345785d8a000087d8dc36206f2000870ae9e7fd96b852872386f26fc1000088",
+      "0ddf5055e4337fd0881bafea3ec90cd29c8801a28279d28a8000875e9bd80a5e6000",
+      "881582b4c9a9db0000883cc3630f46ef480087e337ff7310fc00870422e199ca4a80",
+      "870422e199ca4a808722f7aa4c041800870422e199ca4a808808c2bf28dc3ef00088",
+      "0214e8348c4f000087d9270dc2a714008704229b0d95348087d529ae9e8600008822",
+      "1c0a46e3ac9ea1876a94d74f43000088023b9fa3e27abd2d88058d15e17628000088",
+      "06f05b59d3b200008804fefa17b72400008707d0e36a81800087cf58995ea1428887",
+      "a200f559c2000087498a8a52d9c000874c6222d6abc00087240ccb5bd5aa5f88015f",
+      "b7e2704c9800877c58508723800087044364c5bb000088011c37937e08000087ecf4",
+      "7a281ea800880214e8348c4f00008792e8b594ac8b8c8716b33511bef40086cf0812",
+      "58af90881158e460913d0000880bcbce7f1b15000087f8b0a10e470000873a80727c",
+      "d9d6d4880650a6fb126e2ac08818fae27693b40000871672b45489256e8731bced02",
+      "db00008784f38d03af964987059003dfe68cc88804db732547630000880429d06918",
+      "9e0000870ebe79cc3080008803f374faafbe3f00880279210d016c2000881ab95aa9",
+      "90a06000880165b905826f20008808a2c85ceed480008788a41362b4d000880dd8ef",
+      "b1fd67638a8811a0839022bfbc00882aa1173ca067740087ae153d89fe80008829e9",
+      "31ffd5ae0000882e5b2126ff3cc00087045cdc07c8c0008727ca57357c000087470d",
+      "e4df82000087209dbbfdf6dc0088061b8ef6f9a208008905a9e389b70f52c000881e",
+      "4360bacd2e500087369310accb86f58798ca7e055a4e5788019d7915d1a498008803",
+      "4e6686ede3e00087b1a2bc2ec50000880280a0b8a52658008818cdccb3dc1c280088",
+      "066fb94b5e67d80087470de4df820000880162dfe10504af68880428a40f57413bb5",
+      "8904e0fad4ac64c9a72d87fcb8714bddee7a87fb5d55fee107498807a9a5cde44e55",
+      "6687fd2ae92851ec008801cee802c2fc429888013efa0c880a3330880153c54e35f4",
+      "dc6888044df2f8db17980088029a41408dae00008829a0a27bb2617d1d880147c98b",
+      "a0cf73f687fdc5a90791cac087fbb7e195de726a88012a60d9ec1498b087fc42722e",
+      "674c8087fd010e4a91440088028cf46bdd7d409887fd0e5ff4ec40b387fb8ad9bc93",
+      "2adb89b444990fd4b63c2800880470de4df8200000880f42a70b4d2cb220880153bd",
+      "edad3dd61c878200627e6924008738f5311debec0087b1a2bc2ec5000088055008c2",
+      "8c7a60008804fefa17b72400008801c29d16403a581087b1a2bc2ec5000087470de4",
+      "df820000870c1448303c800087071afd498d00008707d0e36a81800087a0f01c2853",
+      "4000890c6a036eb4bc74000087a6fa40407180008802c68af0bb140000880de0b6b3",
+      "a7640000872fed1562052000871ae7a275486bad872386f26fc100008801988fe405",
+      "2b8000872e2f6e5e14800087e5dc4ea4f7c000875753a518a8e22e870d1c091338a0",
+      "008715d233085c307987f8b0a10e47000087154b813c4d585088011c37937e080000",
+      "87b1a2bc2ec50000880443ba0e080dde668807abd369f80288f887468ebf3c0f7e5a",
+      "8803e2c284391c00008702a106ad22400087b1a2bc2ec5000088250a315be9848000",
+      "87ed400e6219c0008803d239ac0075f858880165c21dd0e1c0008802c68af0bb1400",
+      "00871ff973cafa8000879701b2a34cd890870a9679e25c1000872ba269f721a00087",
+      "0aa87bee53800087e304b62125c000880106fe1bf966600087068c32dbe6b8168806",
+      "f08882108e9d978778ef68a938fc00872f73cb2fdb4f5088012dfb0cb5e880008802",
+      "c68af0bb1400008807a1fe160277000087333b1ff79e73688802a5c6d0d29b4e8288",
+      "096eaa6f2449222087d529ae9e86000088051da3139b985657880d9a5dc72e669a68",
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+      "43fc2c04ee0000872bb2c8eabcc0008829a2241af62c00008725a8a4d29e800087b1",
+      "a2bc2ec5000087354a6ba7a1800088013fbe85edc90000890157329bf98f69000088",
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+      "68e350878e1bc9bf040000875db10acadd602e86036c0b4dcdcc8802c68af0bb1400",
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+      "8abf13800087da475abf00000088068fb000035b600088076598ad11488000878e1b",
+      "c9bf0400008801bfa45519b300008812bb52a141f968728718838370f34000871550",
+      "f7dca70000872386f26fc1000087016bcc41e9000087b58b2de405c000880146d983",
+      "3756000087a200f559c2000087b1a2bc2ec5000087adba4a79844000871c9a5e6155",
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+      "008804fefa17b72400008711c37937e0800087dc5ff4d36ae0008722e9ed8d734bd5",
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+      "a877a3aa55fc0101880533702e777dc440834f4ceb8801aa535d3d0c00008350b6a7",
+      "82740082af00876a94d74f4300008738d7ea4c680000873ff2e795f500008801c972",
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+      "21ff6c155e4fbd878e1bc9bf040000890340aad21b3b700000871606ddfd9b800088",
+      "295b163616aa0000872ba269f721a0008804433881305dde9c8705de8962844f5c87",
+      "0c0443c94738ca870b5e620f4800008802386f26fc1000008803d5dedea5dd400088",
+      "058410a3fa2a94a583fb5b1a8379457188016345785d8a0000837adadd826804880f",
+      "43fc2c04ee00008701bb54fdf2cffb870381828d9df0fe87ae153d89fe800088039c",
+      "d7add005c800876a92b8f520987c88028dbc878335b40087f46d3c488c0000873bf0",
+      "e7562f9800870ae9664a255f3e87b1a2bc2ec50000870e35fa931a00008814d1120d",
+      "7b160000872e2f6e5e1480008801cd24698bd88000877c585087238000870c6f3b40",
+      "b6c00087470de4df8200008718de76816d800087b1a2bc2ec50000880de0b6b3a764",
+      "00008803bf3b91c95b00008709f295cd5f000088020324bb546e8000880237b940db",
+      "1b800088016345785d8a000088016345785d8a000087470de4df820000870487224a",
+      "84935e871c6bf526340000872386f26fc1000087051e564dcb125f8801143fb47538",
+      "671e875da5da5618a40087010884f37406008801c3a6c1d4d45404832a04268806f0",
+      "5b59d3b20000832e08268802c68af0bb14000083fb5b1b870c0e8c20457a3f828806",
+      "8703b0daef8d77a38806f05b59d3b20000871e8da789118000871c8aae2291712687",
+      "dabbde5f9a5e2887121e6c485ac000872b6563077788008802c9cbdfb0db38008738",
+      "c4477c20240088029ec64b0aab880088027f7d0bdb920000872b9cdaf06a0f8d8801",
+      "6345785d8a00008715cfffefbf7050873dd13533178000878964676019da60890c5c",
+      "22b80115100000880214e8348c4f0000880713e24c4373000088162c9b1002213654",
+      "8711c37937e0800088010a7f6a545051748751b660cdd5800088016345785d8a0000",
+      "876e2255f409800088012dfb0cb5e880008905bf0ba6634f6800008808be35a9807f",
+      "000087e5dc4ea4f7c00088061b31ab352c0000873ff2e795f5000087354a6ba7a180",
+      "0088011c37937e080000876a94d74f430000873099e3348700008718de76816d8000",
+      "87da2c620173642c88015985c7c416f00082b4068802fc26a495696432892ebaa730",
+      "eda2b8000083fb5b1c880214e8348c4f000083fb5b1c860c051aa407418806f05b59",
+      "d3b20000860c6827800c51880b1a2bc2ec5000008805e863e500e24000860b209605",
+      "dadd87024439e58886ad8701fd66eac8d8c88805cfd3934e8900008805e73df6cbc9",
+      "08008806d087062e51080087974689ffd63000872fcfc9e8696c0087129e8e9c1d38",
+      "fb8702c8e8ff9f020087f0321d74442019878e1bc9bf040000872386f26fc1000088",
+      "12091ef3d0ad40008766ac659a02400088044d575b885f000088016345785d8a0000",
+      "87b1a2bc2ec5000087b1a2bc2ec5000087b1a2bc2ec5000087b1a2bc2ec5000087d4",
+      "464ef554600088015c2a7b13fd00008802386f26fc1000008718de76816d8000880e",
+      "b5e06245ea0000871ff973cafa800087d4071f617f62d0880429d069189e00008711",
+      "c37937e08000872386f26fc100008898a7d9b8314c00008801118f178fb48000876a",
+      "94d74f430000877da961d8a6fc42870c6f3b40b6c0008712c4e73e94d9cb87417b13",
+      "aa14a7608706e75481ba40008801664f372978e80087b1a2bc2ec50000878e1bc9bf",
+      "040000880aa0f45e97dd488587d8883c83b23e5c88012feed34366c55a87517dea96",
+      "81efc9872386f26fc10000880213800b9cfa4000876a94d74f430000880103591cfc",
+      "9a800087e5266884034000880544408bdfbb3a318768b22c1647880087d5c2fee17e",
+      "4400880138a388a43c00008805bd904cb9f9700087470de4df820000880267b6bcdf",
+      "afca00876a94d74f430000873a9ea99ecb400088016345785d8a0000879d6298db74",
+      "f8008801e3ebe71ee3ab34870c6f3b40b6c00087519abcf34a3166870405a647881a",
+      "318703d7b8fd6c74498703d89d2ac313418703d89d2ac313418703ddd9bc9b7dc187",
+      "03e0e52848ba998703d89d2ac31341880cd2c8c6c7d254328703e558780a19b18802",
+      "ea11e32ad500008803782dace9d900008711c37937e0800087f46d3c488c00008725",
+      "5e5c51db83888802c68af0bb14000088017508f1956a800087167351fc47b6128801",
+      "fc09be0ae180008718017f965c6bc1872386f26fc10000870650de2e292bc9880b31",
+      "f1f2025c1c008722e6e03e460000880890f2095aa214c888081b0d335d920cc888c9",
+      "1ca9f56a2e2ccf873b4fa1acebc53f840260c0e48402738f57835387a08801634578",
+      "5d8a000083546f2e87feac8705a88800878e1bc9bf040000880142805d2280a00083",
+      "fb5b1e88016345785d8a000083fb5b1e87a78df2b8f869e38801ca34ce4d67400088",
+      "046bff6328235000870e0f7720d05c0087470de4df820000876a94d74f4300008805",
+      "2345c117835400880105fe1f7614d80087b1a2bc2ec5000087b73b24ce0efc00882a",
+      "9e9cd3f07ccc008801b48822206b1400871bfc55d8265c008726ca6fa6957c0087da",
+      "315ce6b078008758d15e176280008764bdee90c8a400878e1bc9bf040000876c170f",
+      "ee1b923f87bccbbb1567080087574b32512af9ec87cadf032b4e4c008801c8be7535",
+      "9d200087463a37de7b9800871acd25ca14767c88016345785d8a0000880214e8348c",
+      "4f00008802c68af0bb140000881f399b1438a10000870419e3a92313e98791a94863",
+      "ca80008758d15e1762800088029be90101c600008702dbddc32b39f5871550f7dca7",
+      "000087753d533d96800087b1a2bc2ec500008703e24324884d11880ca485ac5e6180",
+      "0088010a741a4627800087b1a2bc2ec5000087027ca57357c00087305120c0f20000",
+      "8709e217b4f92457876a94d74f43000087047aef9353b0f18779ecfc3cc27fba871e",
+      "8c57c526979488011c37937e0800008806fc8a412fd9b4c888080772fd2059abcb88",
+      "06ef2575a90c14c887022eb88560e000871f9e80ba80400087b1a2bc2ec500008769",
+      "fd794e3b5400876540995819400088058d15e176280000870151a2dd0a8e58868cc8",
+      "cbbd2718870120997d5c74d8870122f15b5e5068880254eb6ac98be40088060428ee",
+      "a0726cf288025136d946724c8687134ca2f322d47b870c0443c94738ca880230cf29",
+      "a6cead63882b05699353b60000821e068802c68af0bb140000865af3107a40008804",
+      "e7cc54b782e00082069887b1a2bc2ec500008803d1792daafd379e880a6587720ee4",
+      "f8a08803d0e1e204bc58588801a9875ef15fe2ce8721a12b68dcc48087123e61743c",
+      "40c487272c3bee09600087038d7ea4c68000877e7a02ea010000880c58adeab6699c",
+      "008801c9a85eec341c00880dd68163f03b832888018a8788fdde4c8b8814d1120d7b",
+      "1600008809f80ff8927e54a4879009abfad5bdec87470de4df82000087da3bfdcaeb",
+      "70ce872386f26fc10000888c2a687ce7720000884db7325476300000872386f26fc1",
+      "0000871be28ed71ea61d871aa535d3d0c00087470de4df820000870aa87bee538000",
+      "8736a5af0d195800880de0b6b3a764000087dfd22a8cd98000872bb2c8eabcc00088",
+      "1c7310237d8d000087e3c99a970ac5788801724634310ecffb87d529ae9e86000088",
+      "0221a0b8bb67309988011c9cb89693a4008708e1bc9bf0400087d7e2fddfac380087",
+      "59c3f6ccb0d32a874a340650678c00880429d069189e000088077551be7010671285",
+      "7e287bc0388803782dace9d90000858b66806e4b88016345785d8a00008644b7c685",
+      "58c687cfc02f26fbcd5087c70b69a22ba34888016345785d8a00008805b8bb3f167f",
+      "5de088030d98d59a96000088030d98d59a96000088030d98d59a96000087670758aa",
+      "7c800088016345785d8a000087c9149bde3f040087ae153d89fe800087b1a2bc2ec5",
+      "00008802c2478bf55900008727593313aca0008740c5faebeaa00087a1771fddd794",
+      "008801e17dda386040008773aa0911f28b2187e982c032b95c8a886f05b59d3b2000",
+      "0087710a97ecf320008726dad0ee3c8000880148a04289b94000873b3c35a991a0de",
+      "8809b6e64a8ec600008806f05b59d3b20000876a94d74f43000087470de4df820000",
+      "8802c68af0bb14000087353f531ef6f00088011c37937e0800008701117c811a71c2",
+      "88044d575b885f000087202f1ccd053000870aa87bee53800087532a5c898c100087",
+      "e69234c5ec40008901881158aa9f1996d7876d0864742820008708e1bc9bf0400087",
+      "0375c45e4f1f79878394b45cb5e8f98770409fc7a4ad69872386f26fc10000881c8b",
+      "ee99fefa80008829a2241af62c00008801ba46dd2d7f994f88026f0a70c8125c0088",
+      "01ca6ff5a82d73fd8803d4009fb8d838c888051c32a739651ae888086c5fe0a750c0",
+      "6f88042b283854af0c5687c6f3b40b6c000087f939b9f26e480087a3fb539e21f33f",
+      "88077e772392b6000082080d856f48b89340880429d069189e0000857295d0000088",
+      "0429d069189e000087b1a2bc2ec500008801b477fb95d6e19c82790488027cb44362",
+      "46e68888057edfe6e30e00008721143131bfa58087100eea826280008802c68af0bb",
+      "14000087eadca295d40bc08801b3fe4cb8c1d29e875d324adfee5c008808c15b5687",
+      "12040088023a3bcfb4a42800880214e8348c4f000088013fbe85edc900008801ca69",
+      "7a00dece5b871e96bfd78420008802c68af0bb140000881bc028b6c498b000881e42",
+      "0c942408f0008745b9be365ca000878e1bc9bf04000087b1a2bc2ec50000870ae966",
+      "4a255f3e874ab77dfbce88008806d1dfee575b867087b1a2bc2ec5000087cf529780",
+      "c6118e8801b477fb95d6e19c87470de4df8200008801793a25be4040008801251950",
+      "19f84000872386f26fc1000088016345785d8a0000870c6f3b40b6c0008801634578",
+      "5d8a00008722572c91ea4e5588010c8c1193e5681c880278d8bc980aae2d878e1bc9",
+      "bf040000890c4e42014d6dac00008806f05b59d3b20000878700cc7577000087498a",
+      "8a52d9c000871f9e80ba804000872386f26fc10000880de0b6b3a764000087ed24c5",
+      "76c1e0008804b0359c32a56c168801635985ec088cef880173b8b22fce489887470d",
+      "e4df82000087a3aeb1f502c4488802c68af0bb140000870221b262dd800089077dc3",
+      "683c72d02000880429d069189e00008824b4f6923a41d76888051787d7788186bb88",
+      "042a06676f2d9fa087a4f78ef76f5467880121ae7c4682c9c28609e6786b6bd38609",
+      "efd7a8dbab88021f49ef7e41e1278802c68af0bb140000880122f6e0a43fd07887ae",
+      "153d89fe80008806ef068e5c7092c087b1a2bc2ec500008807787efa8a6b84008711",
+      "270a58f9c000870645e0692fe0008802a40c017b5700f68758d15e176280008801cd",
+      "da4faccd0000872aa1efb94e0000879982da78799099872386f26fc1000088013fbe",
+      "85edc900008761b31ab352c00088029ec9346d9ef988872386f26fc10000880b19d0",
+      "cfdbd5c000880214e8348c4f000088013fbe85edc9000088058d15e1762800008802",
+      "5bf6196bd10000871ff973cafa80008716b51e037ffc00880429d069189e00008803",
+      "e2c284391c000087af9746059a110f87fbf47beb009960881b4e7d7cb0ea9d038747",
+      "0de4df8200008801b4736c92a8200087fc3e1fb30d800087c4a78a7ac3e6ad870c04",
+      "43c94738ca8801bc16d674ec800088113fa2d8e84ca9008775fd770992376e879fdf",
+      "42f6e4800088183ca64f3bd716738802fef288d0652a28872f5dd656123c488805a0",
+      "9087648aa1488703cb6e6915a800870a9fc0c1bc8000870a963408f75800870aa74d",
+      "4049b8008766f08a7177ad27832a9bb78806f05b59d3b20000832dd3868771671225",
+      "3b000087716712253b00008801f161421c8e0000880342e341423780008801634578",
+      "5d8a000088082bd67afbc0000088b72fd2103b2800008802ba7ea83775c2aa87817f",
+      "14f6102000870fd239236d6300878e1bc9bf04000087bd75a22d17cc008801b2e3f2",
+      "5e8834008801f161421c8e00008801f161421c8e000087da3186cf8680008805109a",
+      "fbcb1d562487b1a2bc2ec50000890340a45730235e000088029d80a15f843a208801",
+      "2eeecb52b54000868bab83b51190872976eb19c136b6876a94d74f430000876220ec",
+      "9ceea2fa880142427206494000880199f7496099700087dc7f78685be400877e936f",
+      "5c17ea668758d15e1762800087ef6c03195be00087894d3de2a27000890111fcc770",
+      "34d991e887b1a2bc2ec50000880853a0d2313c0000873d4318b6881e00870a4d88dd",
+      "d940008803ed0220305a78b6872386f26fc10000872386f26fc10000874436089976",
+      "0c6f88479c00a94104000087f195a3c4ba000087206697785a00008746bbd72822b6",
+      "118804db7325476300008809fd7af31b21f8008802c4383d6df3d000875bb3a1b5b0",
+      "34008766875a68d3bc0087f46164d412680088074211baa1878000880dda214bea69",
+      "c44487470de4df820000880de0b6b3a76400008801f1a4d8434cbf5f8701c6bf5263",
+      "4000872fd345a633ca6888010b5170d823dbcc831ef5fe88016345785d8a00008320",
+      "73ea825704821d048802b4e6142055c40088169a2f45f3e5ace0876a94d74f430000",
+      "87ce230518c88c0087adefff1fca640087ad345e2992cc00880168e909d1d1c80087",
+      "1d5ba7383e855d8711c37937e08000870e0cb529920b00870e0cb529920b00870e0c",
+      "b529920b008702e238aef418e087043c7f8ef8680087045dda08fe9b80870f1ba04f",
+      "e8480087077774b2768cc08713a0f54e62500087033fbb6c0a98c0870310d9e7e31a",
+      "a08702fafd0129ae408702baf467052bc0872714711487800088014b0fbe2ffd3a38",
+      "8802c68af0bb140000886124fee993bc000088010150a5573e8ee888035115c53aa7",
+      "811688c9310ff96afbd9a4877d4d8013bbf630876e7d490483c0008803782dace9d9",
+      "00008802c68af0bb140000880163e4cca7cb9e28887ce66c50e28400008718de7681",
+      "6d8000880f8b0a10e4700000873c6568f12e800088016345785d8a0000880c9d6aaf",
+      "14d4800087470de4df8200008804ba30aebb6aa90087110d9316ec0000880521304d",
+      "638b5cc088027f7d0bdb920000873fe9cf47826000870d00cdb9a6873c8814d1120d",
+      "7b16000087b1a2bc2ec5000087b1a2bc2ec500008803782dace9d900008721a36424",
+      "d7e388874aa41e8474883d8704f4706b9de057876a94d74f43000087114d3d3c0e60",
+      "008801cdda4faccd000087c2281d6449222f872ffd7455a04000879e3bfaf9ec9741",
+    ].join("");
+
+    const txValues: BigNumber[] = RLP.decode(rlpEncodedTxValueSamples).map(
+      (x) => BigNumber.from(x),
+    );
+
+    let pseudoFloatByteCount = 0;
+    let rlpByteCount = 0;
+
+    for (const value of txValues) {
+      const encoded = encodePseudoFloat(value);
+      const [decoded] = await pseudoFloat.decodePublic(encoded);
+      expect(BigNumber.from(value).eq(decoded)).to.eq(true);
+
+      const byteLen = (encoded.length - 2) / 2;
+      pseudoFloatByteCount += byteLen;
+
+      const rlpEncoded = RLP.encode(BigNumber.from(value).toHexString());
+      rlpByteCount += (rlpEncoded.length - 2) / 2;
+    }
+
+    const avgBytesRlp = rlpByteCount / txValues.length;
+    expect(avgBytesRlp.toFixed(2)).to.eq("8.24");
+
+    const avgBytesPseudoFloat = pseudoFloatByteCount / txValues.length;
+    expect(avgBytesPseudoFloat.toFixed(2)).to.eq("4.40");
+    // Almost twice as good.
+    // With economic incentive, most values could be 3 sig figs, which reduces
+    // further to just 2 bytes (>4x as good as RLP).
+  });
+});
diff --git a/contracts/test/vlq-test.ts b/contracts/test/vlq-test.ts
index 55a20415..fd70ad22 100644
--- a/contracts/test/vlq-test.ts
+++ b/contracts/test/vlq-test.ts
@@ -3,7 +3,7 @@ import { expect } from "chai";
 import { ethers } from "hardhat";
 import { VLQ, VLQ__factory } from "../typechain-types";
 
-describe("vlq", function () {
+describe("VLQ", function () {
   let vlq: VLQ;
 
   this.beforeAll(async () => {