Java – GWT: add filtering to CellTable

I've been tasked with implementing sorting & filtering of data displayed in a GWT CellTable.
Thankfully GWT already supports sorting, but it looks like I'll have to hack together my own filtering support.

To be more precise, what I'm trying to support is similar to the filtering offered by Excel, whereby you can click on a drop-down menu in the column headers and (for example) click checkboxes that will allow you to filter the rows based on the values for the filtered column(s). A picture is worth a thousand words:

My question: any suggestions on how to go about implementing this in GWT 2.2? Is it even possible?

One option I'm thinking about is to pass in a custom Header object to CellTable.addColumn(). If it's possible, I'll add a ClickHandler to the Header, and then open a Popup that displays a widget for filtering. Not sure how to implement this without negatively affecting the sorting behavior.

Any suggestions gladly welcome.

Edit:

Thanks to John below, I've got the following FilterableHeader class that allows me to at least put an icon into the header. Unsure how to get a ClickHandler on that icon just yet, as the image is inserted via HTML rather than using GWT widgets.

public class FilterableHeader extends Header<String>
{
    /**
     * Image resources.
     */
    public static interface Resources extends ClientBundle
    {
        ImageResource downArrow();
        ImageResource upArrow();
    }

    private static final Resources RESOURCES = GWT.create(Resources.class);
    private static final int IMAGE_WIDTH = 16;
    private static final String DOWN_ARROW = makeImage(RESOURCES.downArrow());
    private static final String UP_ARROW = makeImage(RESOURCES.upArrow());

    private static String makeImage(ImageResource resource)
    {
        AbstractImagePrototype proto = AbstractImagePrototype.create(resource);
        return proto.getHTML().replace("style='", "style='position:absolute;right:0px;top:0px;");
    }

    private String text;

    public FilterableHeader(String text)
    {
        super(new ClickableTextCell());
        this.text = text;
    }

    @Override
    public String getValue()
    {
        return text;
    }

    @Override
    public void render(Cell.Context context, SafeHtmlBuilder safe)
    {
        int imageWidth = IMAGE_WIDTH;

        StringBuilder sb = new StringBuilder();
        sb.append("<div style='position:relative;cursor:hand;cursor:pointer;");
        sb.append("padding-right:");
        sb.append(imageWidth);
        sb.append("px;'>");
        sb.append(UP_ARROW);
        sb.append("<div>");
        sb.append(text);
        sb.append("</div></div>");

        safe.append(SafeHtmlUtils.fromSafeConstant(sb.toString()));
    }
}