This is a report on joint work with Philippe Michel and Liyang Yang. Let f, resp. g, denote a holomorphic cusp form on U(2,1), resp. U(1,1), of weight (-k, k/2), resp. k, for an even integer k , taken to be at least 260 for technical reasons. We consider the Rankin-Selberg L-function L(s, f x g), which is defined by base changing to GL over the relevant imaginary quadratic field. We average over a family of f with varying square-free levels, and establish a non-vanishing result at the central value, as well as a hybrid subconvexity in the level aspect.