[jQuery] IE and Making dynamically added items draggable?

I need some help with solving the following problem:

I have eight <ul> elements made .droppable() on mouseover (using
Interface), and accepting draggable <li> elements, as so ( Stripped
some non-relevant code ):

$(document).ready(function()
{
        $('body').mouseover(function(event)
        {
                if ($(event.target).is('li.character'))
                {
                        $(event.target).Draggable( ... );
                }
        });

        // Make our group boxes droppable
        $('.group').Droppable( ... );
});

And the function I'm calling on Drop:

var addCharToGroup = function(dragged)
{
        // Which group(droppable) did we drop the draggable on?
        var groupID = $(this).attr('id');

        if(( ($('#' + groupID + ' li.character').size()) == 5 ) && groupID !=
'charter')
        {
                // Should not happen
        }
        else
        {
                // Add the character (li) to the list
                $(dragged).remove().clone().appendTo('#' + groupID + ' ul');
        }
}

This is all working in Firefox, but in IE, once I've dropped and
appended an <li> to a new group, .Draggable() won't be called again.
The .addClass("over") IS being called however, so I know the mouseover
event is working.
Is there a known bug in the Interface Draggable and Internet Explorer,
and if so, is there any workarounds?