Molecular replacement (MR) is a highly-developed and widely-used method of crystal structure determination with alternative approaches to structure solution requiring substantially higher experimental effort. The crucial factors for MR success are: (1) completeness of the search model and its structural similarity to the target structure, (2) completeness and sensitivity of the MR search, and (3) a strategy for testing alternative models and weighting schemes to navigate the combinatorial complexity of the associated assumptions. We identified the biggest obstacles and designed an integrated approach that addresses all identified problems. This advance is based on a novel approach to search models preparation and better conceptual approaches to combinatorial problems of testing multiple hypotheses in MR search.