diff --git a/src/effects.js b/src/effects.js
index b0675395..0b08bc2d 100644
--- a/src/effects.js
+++ b/src/effects.js
@@ -189,7 +189,7 @@ jQuery.fn.extend({
 
 					if ( parts ) {
 						var end = parseFloat( parts[2] ),
-							unit = parts[3] || "px";
+							unit = parts[3] || jQuery.cssNumber[ name ] ? "" : "px";
 
 						// We need to compute starting value
 						if ( unit !== "px" ) {
@@ -348,7 +348,7 @@ jQuery.fx.prototype = {
 		this.startTime = jQuery.now();
 		this.start = from;
 		this.end = to;
-		this.unit = unit || this.unit || "px";
+		this.unit = unit || this.unit || jQuery.cssNumber[ this.prop ] ? "" : "px";
 		this.now = this.start;
 		this.pos = this.state = 0;
 
diff --git a/test/unit/effects.js b/test/unit/effects.js
index bab4f256..7fb1c7d8 100644
--- a/test/unit/effects.js
+++ b/test/unit/effects.js
@@ -919,3 +919,13 @@ test("hide hidden elements, with animation (bug #7141)", function() {
 		});
 	});
 });
+
+test("animate unit-less properties (#4966)", 2, function() {
+	stop();
+	var div = jQuery( "<div style='z-index: 0'></div>" ).appendTo( "body" );
+	equal( div.css( "z-index" ), "0", "z-index is 0" );
+	div.animate({ zIndex: 2 }, function() {
+		equal( div.css( "z-index" ), "2", "z-index is 2" );
+		start();
+	});
+});