diff --git a/javascript/src/collection.js b/javascript/src/collection.js
index 6524f29fd..2af3bec7b 100644
--- a/javascript/src/collection.js
+++ b/javascript/src/collection.js
@@ -21,11 +21,12 @@ goog.requireType('ee.Geometry');
  * @param {ee.Function} func The same argument as in ee.ComputedObject().
  * @param {Object} args The same argument as in ee.ComputedObject().
  * @param {string?=} opt_varName The same argument as in ee.ComputedObject().
+ * @param {boolean?=} opt_unbound The same argument as in ee.ComputedObject().
  * @constructor
  * @extends {ee.Element}
  */
-ee.Collection = function(func, args, opt_varName) {
-  ee.Collection.base(this, 'constructor', func, args, opt_varName);
+ee.Collection = function(func, args, opt_varName, opt_unbound) {
+  ee.Collection.base(this, 'constructor', func, args, opt_varName, opt_unbound);
   ee.Collection.initialize();
 };
 goog.inherits(ee.Collection, ee.Element);
@@ -219,8 +220,12 @@ ee.Collection.prototype.elementType = function() {
  * @export
  */
 ee.Collection.prototype.map = function(algorithm, opt_dropNulls) {
-  var elementType = this.elementType();
-  var withCast = function(e) { return algorithm(new elementType(e)); };
+  const elementType = this.elementType();
+  const withCast = function(e) {
+    const el = /** @type {!ee.ComputedObject} */ (new elementType(e));
+    el.unbound = true;
+    return algorithm(el);
+  };
   return this.castInternal(ee.ApiFunction._call(
       'Collection.map', this, withCast, opt_dropNulls));
 };
@@ -241,8 +246,12 @@ ee.Collection.prototype.map = function(algorithm, opt_dropNulls) {
  * @export
  */
 ee.Collection.prototype.iterate = function(algorithm, opt_first) {
-  var first = (opt_first !== undefined) ? opt_first : null;
-  var elementType = this.elementType();
-  var withCast = function(e, p) { return algorithm(new elementType(e), p); };
+  const first = (opt_first !== undefined) ? opt_first : null;
+  const elementType = this.elementType();
+  const withCast = function(e, p) {
+    const el = /** @type {!ee.ComputedObject} */ (new elementType(e));
+    el.unbound = true;
+    return algorithm(el, p);
+  };
   return ee.ApiFunction._call('Collection.iterate', this, withCast, first);
 };
diff --git a/javascript/src/computedobject.js b/javascript/src/computedobject.js
index 9be9616e1..d134802c9 100644
--- a/javascript/src/computedobject.js
+++ b/javascript/src/computedobject.js
@@ -39,11 +39,13 @@ goog.requireType('ee.Function');
  *     and both 'func' and 'args' must be null. If all arguments are null, the
  *     object is considered an unnamed variable, and a name will be generated
  *     when it is included in an ee.CustomFunction.
+ * @param {?boolean=} opt_unbound Whether the object is unbound, i.e., called
+ *     from a mapped or iterated function.
  * @constructor
  * @extends {ee.Encodable}
  * @template T
  */
-ee.ComputedObject = function(func, args, opt_varName) {
+ee.ComputedObject = function(func, args, opt_varName, opt_unbound) {
   // Constructor safety.
   if (!(this instanceof ee.ComputedObject)) {
     return ee.ComputedObject.construct(ee.ComputedObject, arguments);
@@ -76,6 +78,12 @@ ee.ComputedObject = function(func, args, opt_varName) {
    * @protected
    */
   this.varName = opt_varName || null;
+
+  /**
+   * Whether the computed object is an unbound variable.
+   * @type {boolean}
+   */
+  this.unbound = !!opt_unbound;
 };
 goog.inherits(ee.ComputedObject, ee.Encodable);
 // Exporting manually to avoid marking the class public in the docs.
@@ -153,14 +161,20 @@ ee.ComputedObject.prototype.encodeCloudValue = function(serializer) {
   if (this.isVariable()) {
     const name = this.varName || serializer.unboundName;
     if (!name) {
-      // We are trying to call getInfo() or make some other server call inside a
-      // function passed to collection.map() or .iterate(), and the call uses
-      // one of the function arguments. The argument will be unbound outside of
-      // the map operation and cannot be evaluated. See the Count Functions case
-      // in customfunction.js for details on the unboundName mechanism.
-      // TODO(user): Report the name of the offending argument.
-      throw new Error(
-          'A mapped function\'s arguments cannot be used in client-side operations');
+      if (this.unbound) {
+        // We are trying to call getInfo() or make some other server call inside
+        // a function passed to collection.map() or .iterate(), and the call
+        // uses one of the function arguments. The argument will be unbound
+        // outside of the map operation and cannot be evaluated. See the Count
+        // Functions case in customfunction.js for details on the unboundName
+        // mechanism.
+        // TODO(user): Report the name of the offending argument.
+        throw new Error(`A mapped function's arguments (${
+            this.name()}) cannot be used in client-side operations`);
+      } else {
+        throw new Error(
+            `Invalid cast to ${this.name()} from a client-side object`);
+      }
     }
     return ee.rpc_node.argumentReference(name);
   } else {
diff --git a/javascript/src/dictionary.js b/javascript/src/dictionary.js
index 54702e3d6..20ae5e4ad 100644
--- a/javascript/src/dictionary.js
+++ b/javascript/src/dictionary.js
@@ -51,7 +51,7 @@ ee.Dictionary = function(opt_dict) {
     if (opt_dict instanceof ee.ComputedObject && opt_dict.func &&
         opt_dict.func.getSignature()['returns'] == 'Dictionary') {
       // If it's a call that's already returning a Dictionary, just cast.
-      ee.Dictionary.base(this, 'constructor', opt_dict.func, opt_dict.args, opt_dict.varName);
+      ee.Dictionary.base(this, 'constructor', opt_dict.func, opt_dict.args, opt_dict.varName, opt_dict.unbound);
     } else {
       // Delegate everything else to the server-side constructor.
       ee.Dictionary.base(
diff --git a/javascript/src/element.js b/javascript/src/element.js
index 5dd736fe9..e769ffe62 100644
--- a/javascript/src/element.js
+++ b/javascript/src/element.js
@@ -19,11 +19,12 @@ goog.requireType('ee.Function');
  * @param {ee.Function} func The same argument as in ee.ComputedObject().
  * @param {Object} args The same argument as in ee.ComputedObject().
  * @param {string?=} opt_varName The same argument as in ee.ComputedObject().
+ * @param {boolean?=} opt_unbound The same argument as in ee.ComputedObject().
  * @constructor
  * @extends {ee.ComputedObject}
  */
-ee.Element = function(func, args, opt_varName) {
-  ee.Element.base(this, 'constructor', func, args, opt_varName);
+ee.Element = function(func, args, opt_varName, opt_unbound) {
+  ee.Element.base(this, 'constructor', func, args, opt_varName, opt_unbound);
   ee.Element.initialize();
 };
 goog.inherits(ee.Element, ee.ComputedObject);
diff --git a/javascript/src/feature.js b/javascript/src/feature.js
index 2d4ecd5dc..12195a471 100644
--- a/javascript/src/feature.js
+++ b/javascript/src/feature.js
@@ -57,7 +57,7 @@ ee.Feature = function(geometry, opt_properties) {
     });
   } else if (geometry instanceof ee.ComputedObject) {
     // A custom object to reinterpret as a Feature.
-    ee.Feature.base(this, 'constructor', geometry.func, geometry.args, geometry.varName);
+    ee.Feature.base(this, 'constructor', geometry.func, geometry.args, geometry.varName, geometry.unbound);
   } else if (geometry['type'] == 'Feature') {
     // Try to convert a GeoJSON Feature.
     var properties = geometry['properties'] || {};
diff --git a/javascript/src/filter.js b/javascript/src/filter.js
index be20ddbb6..4cd080394 100644
--- a/javascript/src/filter.js
+++ b/javascript/src/filter.js
@@ -65,7 +65,7 @@ ee.Filter = function(opt_filter) {
     }
   } else if (opt_filter instanceof ee.ComputedObject) {
     // Actual filter object.
-    ee.Filter.base(this, 'constructor', opt_filter.func, opt_filter.args, opt_filter.varName);
+    ee.Filter.base(this, 'constructor', opt_filter.func, opt_filter.args, opt_filter.varName, opt_filter.unbound);
     this.filter_ = [opt_filter];
   } else if (opt_filter === undefined) {
     // A silly call with no arguments left for backward-compatibility.
diff --git a/javascript/src/geometry.js b/javascript/src/geometry.js
index 0626ec9f5..bea753d06 100644
--- a/javascript/src/geometry.js
+++ b/javascript/src/geometry.js
@@ -87,7 +87,7 @@ ee.Geometry = function(geoJson, opt_proj, opt_geodesic, opt_evenOdd) {
           'Setting the CRS, geodesic, or evenOdd flag on a computed Geometry ' +
           'is not supported.  Use Geometry.transform().');
     } else {
-      ee.Geometry.base(this, 'constructor', geoJson.func, geoJson.args, geoJson.varName);
+      ee.Geometry.base(this, 'constructor', geoJson.func, geoJson.args, geoJson.varName, geoJson.unbound);
       return;
     }
   }
diff --git a/javascript/src/image.js b/javascript/src/image.js
index 041acf986..482cc6a06 100644
--- a/javascript/src/image.js
+++ b/javascript/src/image.js
@@ -77,7 +77,7 @@ ee.Image = function(opt_args) {
                   {'value': opt_args});
       } else {
         // A custom object to reinterpret as an Image.
-        ee.Image.base(this, 'constructor', opt_args.func, opt_args.args, opt_args.varName);
+        ee.Image.base(this, 'constructor', opt_args.func, opt_args.args, opt_args.varName, opt_args.unbound);
       }
     } else {
       throw Error('Unrecognized argument type to convert to an Image: ' +
diff --git a/javascript/src/imagecollection.js b/javascript/src/imagecollection.js
index 7d9a1031c..59fa4b2da 100644
--- a/javascript/src/imagecollection.js
+++ b/javascript/src/imagecollection.js
@@ -70,7 +70,7 @@ ee.ImageCollection = function(args) {
     });
   } else if (args instanceof ee.ComputedObject) {
     // A custom object to reinterpret as an ImageCollection.
-    ee.ImageCollection.base(this, 'constructor', args.func, args.args, args.varName);
+    ee.ImageCollection.base(this, 'constructor', args.func, args.args, args.varName, args.unbound);
   } else {
     throw Error('Unrecognized argument type to convert to an ' +
                 'ImageCollection: ' + args);
diff --git a/javascript/src/list.js b/javascript/src/list.js
index 4fac2d91b..6a439ddd5 100644
--- a/javascript/src/list.js
+++ b/javascript/src/list.js
@@ -45,7 +45,7 @@ ee.List = function(list) {
     ee.List.base(this, 'constructor', null, null);
     this.list_ = /** @type {IArrayLike} */ (list);
   } else if (list instanceof ee.ComputedObject) {
-    ee.List.base(this, 'constructor', list.func, list.args, list.varName);
+    ee.List.base(this, 'constructor', list.func, list.args, list.varName, list.unbound);
     this.list_ = null;
   } else {
     throw Error('Invalid argument specified for ee.List(): ' + list);
diff --git a/javascript/src/number.js b/javascript/src/number.js
index d689c1c46..f8f2dbe26 100644
--- a/javascript/src/number.js
+++ b/javascript/src/number.js
@@ -43,7 +43,7 @@ ee.Number = function(number) {
     ee.Number.base(this, 'constructor', null, null);
     this.number_ = /** @type {number} */ (number);
   } else if (number instanceof ee.ComputedObject) {
-    ee.Number.base(this, 'constructor', number.func, number.args, number.varName);
+    ee.Number.base(this, 'constructor', number.func, number.args, number.varName, number.unbound);
     this.number_ = null;
   } else {
     throw Error('Invalid argument specified for ee.Number(): ' + number);
diff --git a/javascript/src/string.js b/javascript/src/string.js
index 0fba3bbfe..798228a19 100644
--- a/javascript/src/string.js
+++ b/javascript/src/string.js
@@ -46,9 +46,9 @@ ee.String = function(string) {
     this.string_ = null;
     if (string.func && string.func.getSignature()['returns'] == 'String') {
       // If it's a call that's already returning a String, just cast.
-      ee.String.base(this, 'constructor', string.func, string.args, string.varName);
+      ee.String.base(this, 'constructor', string.func, string.args, string.varName, string.unbound);
     } else {
-      ee.String.base(this, 'constructor', new ee.ApiFunction('String'), {'input': string}, null);
+      ee.String.base(this, 'constructor', new ee.ApiFunction('String'), {'input': string}, null, string.unbound);
     }
   } else {
     throw Error('Invalid argument specified for ee.String(): ' + string);