How do I add a custom icon to a standard jQuery UI theme?

It is easy to use one of the icons available from the standard icon set:

$("#myButton").button({icons: {primary: "ui-icon-locked"}});

But what if I want to add one of my own icons that is not part of the framework icon set?

I thought it would be as easy as giving it your own CSS class with a background image, but that doesn't work:

.fw-button-edit {
    background-image: url(edit.png);
}

Any suggestions?