Lengthening short Urls in C#

If you deal with Twitter APIs, sooner or later, you'll probably want to lengthen those short URLs back to long URLs. There's a couple of services you can use to do this but it's really quite easy so you might as well do it yourself. The code below follows each redirect until it reaches a real page (or an error), it then returns the last URL it finds.

private string UrlLengthen(string url)
{
	string newurl = url;
	bool redirecting = true;
	while (redirecting) 
	{
		try
		{
			HttpWebRequest request = (HttpWebRequest)WebRequest.Create(newurl);
			request.AllowAutoRedirect = false; 
			request.UserAgent = "Mozilla/5.0 (Windows; U; Windows NT 6.1; en-US; rv:1.9.1.3) Gecko/20090824 Firefox/3.5.3 (.NET CLR 4.0.20506)";
			HttpWebResponse response = (HttpWebResponse)request.GetResponse(); 
			if ((int)response.StatusCode == 301 || (int)response.StatusCode == 302)
			{
				string uriString = response.Headers["Location"];
				Log.Debug("Redirecting" + newurl + " to " + uriString + " because " + response.StatusCode);
				newurl = uriString; // and keep going 
			}
			else
			{
				Log.Debug("Not redirecting " + url + " because " + response.StatusCode);
				redirecting = false; 
			}
		}
		catch (Exception ex) 
		{ 
			ex.Data.Add("url", newurl);
			Exceptions.ExceptionRecord.ReportCritical(ex);
			redirecting = false; 
		} 
	}
	return newurl;
}