How can I fix the Kerberos double-hop issue?

I’m having some trouble calling a web service from within a web application and I was hoping someone here might be able to help. From what I can tell, this seems to have something to do with the Kerberos double-hop issue. However, if it is, I’m not sure what to do to actually fix the problem. To make things harder, I don’t have the proper permissions to make changes to Active Directory accounts, so I need to know what to ask for when requesting changes. In my situation, I need to pass the credentials (Integrated Windows Authentication) from a web application onto a backend web service so that the web service runs under the proper user context.