diff --git a/lib/json0.js b/lib/json0.js
index 9f538ee..912d005 100644
--- a/lib/json0.js
+++ b/lib/json0.js
@@ -65,13 +65,22 @@ json.create = function(data) {
   return data === undefined ? null : clone(data);
 };
 
-json.invertComponent = function(c) {
+json.invertComponent = function(c, doc) {
   var c_ = {p: c.p};
 
+  var hasDoc = typeof doc !== 'undefined';
+  for (var i = 0; i < c.p.length; i++) {
+    var key = c.p[i];
+    doc = doc && doc[key];
+  }
+
   // handle subtype ops
   if (c.t && subtypes[c.t]) {
     c_.t = c.t;
-    c_.o = subtypes[c.t].invert(c.o);
+    var subtype = subtypes[c.t];
+    if (hasDoc && typeof subtype.invertWithDoc === 'function') c_.o = subtype.invertWithDoc(c.o, doc);
+    else if (typeof subtype.invert === 'function') c_.o = subtype.invert(c.o);
+    else throw new Error("Subtype '" + c.t + "' is not invertible");
   }
 
   if (c.si !== void 0) c_.sd = c.si;
@@ -99,6 +108,15 @@ json.invert = function(op) {
   return iop;
 };
 
+json.invertWithDoc = function(op, doc) {
+  var op_ = op.slice().reverse();
+  var iop = [];
+  for (var i = 0; i < op_.length; i++) {
+    iop.push(json.invertComponent(op_[i], doc));
+  }
+  return iop;
+}
+
 json.checkValidOp = function(op) {
   for (var i = 0; i < op.length; i++) {
     if (!isArray(op[i].p)) throw new Error('Missing path');
diff --git a/test/json0.coffee b/test/json0.coffee
index e2ee6df..019efdb 100644
--- a/test/json0.coffee
+++ b/test/json0.coffee
@@ -222,6 +222,27 @@ genTests = (type) ->
         assert.deepEqual [{p:[100], si:'hi'}], type.compose [{p:[100], si:'h'}], [{p:[101], si:'i'}]
         assert.deepEqual [{p:[], t:'text0', o:[{p:100, i:'hi'}]}], type.compose [{p:[], t:'text0', o:[{p:100, i:'h'}]}], [{p:[], t:'text0', o:[{p:101, i:'i'}]}]
 
+    describe '#invertWithDoc()', ->
+      it 'passes the doc to the subtype', ->
+        op = null
+        doc = null
+
+        type.registerSubtype
+          name: 'invertible'
+          invertWithDoc: (o, d) ->
+            op = o
+            doc = d
+
+        type.invertWithDoc [{p: ['foo', 'bar'], t: 'invertible', o: [{increment: 1}]}], {foo: {bar: 5}}
+        assert.deepEqual [{increment: 1}], op
+        assert.deepEqual 5, doc
+
+      it 'throws if the subtype does not support inversion', ->
+        type.registerSubtype
+          name: 'not-invertible'
+
+        assert.throws -> type.invertWithDoc [{p: ['foo'], t: 'not-invertible', o: [{increment: 1}]}], {foo: 5}
+
     it 'moves ops on a moved element with the element', ->
       assert.deepEqual [{p:[10], ld:'x'}], type.transform [{p:[4], ld:'x'}], [{p:[4], lm:10}], 'left'
       assert.deepEqual [{p:[10, 1], si:'a'}], type.transform [{p:[4, 1], si:'a'}], [{p:[4], lm:10}], 'left'