diff --git a/tests/unit/core/core.js b/tests/unit/core/core.js
index 7a78ae34d..1026c5b0b 100644
--- a/tests/unit/core/core.js
+++ b/tests/unit/core/core.js
@@ -153,4 +153,14 @@ test( "outerHeight(true) - setter", function() {
 	equal( el.height(), 32, "height set properly when hidden" );
 });
 
+test( "uniqueId / removeUniqueId", function() {
+	var el = $( "img" ).eq( 0 );
+
+	equal( el.attr( "id" ), undefined, "element has no initial id" );
+	el.uniqueId();
+	ok( /ui-id-\d+$/.test( el.attr( "id" ) ), "element has generated id" );
+	el.removeUniqueId();
+	equal( el.attr( "id" ), undefined, "unique id has been removed from element" );
+});
+
 })( jQuery );
diff --git a/ui/jquery.ui.core.js b/ui/jquery.ui.core.js
index d8fff91e1..a511de24b 100644
--- a/ui/jquery.ui.core.js
+++ b/ui/jquery.ui.core.js
@@ -9,6 +9,9 @@
  */
 (function( $, undefined ) {
 
+var uuid = 0,
+	runiqueId = /^ui-id-\d+$/;
+
 // prevent duplicate loading
 // this is only a problem because we proxy existing functions
 // and we don't want to double proxy them
@@ -107,6 +110,22 @@ $.fn.extend({
 		return 0;
 	},
 
+	uniqueId: function() {
+		return this.each(function() {
+			if ( !this.id ) {
+				this.id = "ui-id-" + (++uuid);
+			}
+		});
+	},
+
+	removeUniqueId: function() {
+		return this.each(function() {
+			if ( runiqueId.test( this.id ) ) {
+				$( this ).removeAttr( "id" );
+			}
+		});
+	},
+
 	disableSelection: function() {
 		return this.bind( ( $.support.selectstart ? "selectstart" : "mousedown" ) +
 			".ui-disableSelection", function( event ) {