Let chi_q be real characters of large conductor q. Let f be a fixed GL(2) cusp form of trivial central character. In 2000, by using a moment method, Conrey and Iwaniec obtained the best known subconvexity bounds for self-dual L-functions L(\chi_q,1/2) and L(f\times\chi_q,1/2) in the large q-aspect. This approach was later adapted by Xiaoqing Li to give the first subconvexity bounds for GL(3)xGL(2) self-dual L-functions in the large GL(2) spectral aspect. In this talk, we revisit Li's work and explain how her bounds can be improved to the limit of this method. Some Motohashi-type formulae surrounding these problems will also be discussed. Joint work with Ramon Nunes and Zhi Qi.