Customize jquery ui selectmenu button icon

What is the simplest way to customize the jquery ui selectmenu button icon (not the dropdown icons) with a custom icon NOT defined by default in the jQuery UI CSS Framework.

I see many examples for customizing jquery ui button icons using CSS, but not the selectmenu button icon.

<!doctype html>
<html lang="en">
<head>
  <title>SelectMenu Button Test</title>
  <link rel="stylesheet" href="//code.jquery.com/ui/1.11.2/themes/smoothness/jquery-ui.css">
  <script src="//code.jquery.com/jquery-1.10.2.js"></script>
  <script src="//code.jquery.com/ui/1.11.2/jquery-ui.js"></script>

  <script>
  $(function() {
    $( "#buttonone" ).selectmenu({ icons: { button: "ui-icon-triangle-2-n-s" } });  
 //Replace with custom selectmenu button icon

    $( "#buttontwo" ).selectmenu({ icons: { button: "ui-icon-triangle-1-s" } }); 
//Replace with a second custom selectmenu button icon
  });
  </script>
</head>
<body>
     <select name="buttonone" id="buttonone">
            <option>All fields</option>
            <option>Field one</option>
            <option>Field two</option>
     </select>

     <select name="buttontwo" id="buttontwo">
            <option>All options</option>
            <option>Option one</option>
            <option>Option two</option>
     </select>

</body>
</html>

Solution

Yes, you can easily use custom styling on a button by supplying a custom class name, like this:

$( "#selectId" ).selectmenu({ icons: { button: "custom-icon" } });

Then you just add styling rules to your CSS for that class, like this:

.ui-state-default .ui-icon.custom-icon {
    background-image: url([your custom image]);
}

Simple JSFiddle example: http://jsfiddle.net/CaseyRule/f7q8sp43/1/