diff --git a/jsonpointer.js b/jsonpointer.js
index e1f080e..7cfaec0 100644
--- a/jsonpointer.js
+++ b/jsonpointer.js
@@ -39,7 +39,7 @@ function setter (obj, pointer, value) {
   }
 
   var oldValue = obj[part]
-  if (value === null) delete obj[part]
+  if (value === undefined) delete obj[part]
   else obj[part] = value
   return oldValue
 }
@@ -65,7 +65,7 @@ function get (obj, pointer) {
   for (var p = 1; p < len;) {
     obj = obj[untilde(pointer[p++])]
     if (len === p) return obj
-    if (typeof obj !== 'object') return null
+    if (typeof obj !== 'object') return undefined
   }
 }
 
diff --git a/test.js b/test.js
index 8e48b46..e3d9963 100644
--- a/test.js
+++ b/test.js
@@ -40,10 +40,25 @@ assert.equal(jsonpointer.get(obj, '/d/e/0/a'), 4)
 assert.equal(jsonpointer.get(obj, '/d/e/1/b'), 5)
 assert.equal(jsonpointer.get(obj, '/d/e/2/c'), 6)
 
+// can set `null` as a value
+assert.equal(jsonpointer.set(obj, '/f/g/h/foo/0', null), 'test')
+assert.strictEqual(jsonpointer.get(obj, '/f/g/h/foo/0'), null)
+assert.equal(jsonpointer.set(obj, '/b/c', null), 3)
+assert.strictEqual(jsonpointer.get(obj, '/b/c'), null)
+
 assert.equal(jsonpointer.get(obj, ''), obj)
 assert.throws(function () { jsonpointer.get(obj, 'a') }, validateError)
 assert.throws(function () { jsonpointer.get(obj, 'a/') }, validateError)
 
+// can unset values with `undefined`
+jsonpointer.set(obj, '/a', undefined)
+assert.strictEqual(jsonpointer.get(obj, '/a'), undefined)
+jsonpointer.set(obj, '/d/e/1', undefined)
+assert.strictEqual(jsonpointer.get(obj, '/d/e/1'), undefined)
+
+// returns `undefined` when path extends beyond any existing objects
+assert.strictEqual(jsonpointer.get(obj, '/x/y/z'), undefined)
+
 function validateError (err) {
   if ((err instanceof Error) && /Invalid JSON pointer/.test(err.message)) {
     return true