Modify HTTP Headers for a JSONP request

I am using jquery to build a request to the Twitter Search API. I am using jsonp, as is needed for cross-domain requests. However, the Twitter API specifies that you should set a unique User-Agent for these requests, and limits your requests if you do not. The problem is, I see no way of setting this header via jquery.

This is the code I am using:

$.ajax({
    url: 'http://search.twitter.com/search.json',
    dataType: 'jsonp',
    type: 'get',
    data: { q: 'twitter' },
    success: function(data) {
        alert(data.results);
    }
});

I have tried using the beforeSend method, but it appears that this event is not firing. Can anyone come up with any way of solving this problem?

Thanks.