By a double of a free group, we mean a graph of two free groups with one cyclic edge group which maps isomorphically into both of the vertex groups. We prove that every one-ended doubles of rank-two free groups contains hyperbolic surface groups. We also explain how this would generalize to an arbitrary graph of free groups with cyclic edge groups if a finite graph theoretic conjecture is resolved. This finite graph theoretic conjecture is equivalent to the existence of a certain van Kampen diagram on a closed surface. This talk includes a joint work with Henry Wilton and also one with Sang-il Oum.