diff --git a/tests/unit/draggable/draggable_core.js b/tests/unit/draggable/draggable_core.js
index 7df0969b1a5..dd526e5ec85 100644
--- a/tests/unit/draggable/draggable_core.js
+++ b/tests/unit/draggable/draggable_core.js
@@ -274,17 +274,34 @@ asyncTest( "#4261: active element should blur when mousing down on a draggable",
 });
 
 test( "ui-draggable-handle assigned to appropriate element", function() {
-	expect( 4 );
+	expect( 5 );
 
-	var element = $( "<div><p></p></div>" ).appendTo( "#qunit-fixture" ).draggable();
+	var p = $( "<p>" ).appendTo( "#qunit-fixture" ),
+		element = $( "<div><p></p></div>" ).appendTo( "#qunit-fixture" ).draggable();
 	ok( element.hasClass( "ui-draggable-handle" ), "handle is element by default" );
 
 	element.draggable( "option", "handle", "p" );
 	ok( !element.hasClass( "ui-draggable-handle" ), "removed from element" );
 	ok( element.find( "p" ).hasClass( "ui-draggable-handle" ), "added to handle" );
 
+	ok( !p.hasClass( "ui-draggable-handle" ),
+		"ensure handle class name is constrained within the draggble (#10212)" );
+
 	element.draggable( "destroy" );
 	ok( !element.find( "p" ).hasClass( "ui-draggable-handle" ), "removed in destroy()" );
 });
 
+test( "ui-draggable-handle managed correctly in nested draggables", function() {
+	expect( 4 );
+	var parent = $( "<div><div></div></div>" ).draggable().appendTo( "#qunit-fixture" ),
+		child = parent.find( "div" ).draggable();
+
+	ok( parent.hasClass( "ui-draggable-handle" ), "parent has class name on init" );
+	ok( child.hasClass( "ui-draggable-handle" ), "child has class name on init" );
+
+	parent.draggable( "destroy" );
+	ok( !parent.hasClass( "ui-draggable-handle" ), "parent loses class name on destroy" );
+	ok( child.hasClass( "ui-draggable-handle" ), "child retains class name on destroy" );
+});
+
 })( jQuery );
diff --git a/ui/draggable.js b/ui/draggable.js
index c27fc8733e7..5f29f4cf8b3 100644
--- a/ui/draggable.js
+++ b/ui/draggable.js
@@ -78,6 +78,7 @@ $.widget("ui.draggable", $.ui.mouse, {
 	_setOption: function( key, value ) {
 		this._super( key, value );
 		if ( key === "handle" ) {
+			this._removeHandleClassName();
 			this._setHandleClassName();
 		}
 	},
@@ -314,14 +315,13 @@ $.widget("ui.draggable", $.ui.mouse, {
 	},
 
 	_setHandleClassName: function() {
-		this._removeHandleClassName();
-		$( this.options.handle || this.element ).addClass( "ui-draggable-handle" );
+		this.handleElement = this.options.handle ?
+			this.element.find( this.options.handle ) : this.element;
+		this.handleElement.addClass( "ui-draggable-handle" );
 	},
 
 	_removeHandleClassName: function() {
-		this.element.find( ".ui-draggable-handle" )
-			.addBack()
-			.removeClass( "ui-draggable-handle" );
+		this.handleElement.removeClass( "ui-draggable-handle" );
 	},
 
 	_createHelper: function(event) {