In the wake of the replication crisis, scholars have repeatedly argued that one reason for low (and varying) replication rates is that theories and hypotheses are under-specified: most theories do not sufficiently indicate the conditions under which their hypothesized phenomena can or cannot be expected. The proposed remedy for this problem is to search for these conditions systematically and exhaustively – that is, to make a theory or hypothesis more specific. We will argue that the undoubtedly valuable strive to overcome under-specification should be complemented by tackling over-specification. Over-specification characterizes instances of hypotheses or phenomena involving assumptions that could be dropped or replaced by simpler versions without noticeable loss in explanatory power. We will review a series of examples from cognitive and social cognitive psychology (including one original study) to demonstrate the benefits and limitations of this strive for simplification and parsimony. Tackling over-specification proves to be a valuable strategy to gain theoretical insight solidly and efficiently, and to improve cumulativeness, unity, and communicability of evidence and hypotheses.