How to design software when using BDD?

Question

I'm working on a project right now and it's my first project using BDD. Up till now, the user stories have proven themselves a very valuable weapon to understand requirements and to specify the solution in a comprehensive, easy to understand language.

My question is this: now that my user stories are complete, how do I design my solution? I understand that I derive behavior tests from my user stories, and I have to do UI design, but am I supposed to use good ol' UML? I'm under the impression that when using user stories, UML is left out; is this correct?