I will describe an algorithm to construct one-loop supergravity four-point amplitudes in AdS_5xS^5, which are dual to a large N expansion of N=4 super Yang-Mills at strong coupling. A couple of subtle features are crucial for this construction to work, such as the correct identification of single-particle states in the bulk with their CFT duals (which is relevant for any AdS/CFT setting), or the presence of a non-trivial sector of protected operators in the OPE at low twists.