Complexity in a theoretical model may or may not be associated with a high level of arbitrariness, depending on how the model is constructed. In this paper I use examples from cardiac electrophysiology to illustrate two techniques for maintaining significance in complex simulations. First, the approaches of analysis and synthesis are compared as methods of constructing models of complex systems. When a model is constructed by synthesis of known principles, facts, and subunits, it may have any degree of complexity without losing significance; the same is not true for analysis models. Significance can also be maintained by assembling a limited model to test a specific hypothesis of mechanism.