Set Headers with jQuery.ajax and JSONP?

I am trying to access google docs with jQuery. Here's what I have so far:

var token = "my-auth-token";
$.ajax({
  url: "http://docs.google.com/feeds/documents/private/full?max-results=1&alt=json",
  dataType: 'jsonp',
  beforeSend: function(xhr) {
    xhr.setRequestHeader("Authorization", "GoogleLogin auth=" + token);
  },
  success: function(data, textStatus, XMLHttpRequest) {
  },
  error: function(XMLHttpRequest, textStatus, errorThrown) {
  }
});

It doesn't allow me to set headers if I set the dataType to jsonp (from Make Cross Domain Ajax Requests with jQuery). If I leave out jsonp, I can't make the cross-domain request. If I use jQuery.getJSON, I can't pass in any headers...

Is there any way to define custom headers when making a cross-domain ajax request (in jQuery)?

This is not possible.

A JSONP request works by creating a <script> element with its src attribute set to the request URL.
You cannot add custom headers to the HTTP request sent by a <script> element.