jQuery ajax - avoiding error() callback when statusCode() callback invoked

I'm using jQuery.ajax() to connect to my back end service. I have configured an error() handler and a statusCode() handler. They both work fine, but when my statusCode handler gets fired the error handler also fires (the error handler is actually fired first). I would prefer this not to happen. I am assuming this is possible without having to hack the error handler code?

My code looks something like this:

$.ajax({
    ...
    error: function(...) { 
        // process a general type of error here
    },
    statusCode: {
        401: function() {
            // process a specific authentication failure
        }
    }                 
});

So how can I avoid the error() handler firing when the HTTP status code is 401?

Thanks for bothering to read!