Here we introduce a new design framework for synthetic biology that exploits the advantages of Bayesian model selection. We will argue that the difference between inference and design is that in the former we try to reconstruct the system that has given rise to the data that we observe, whereas in the latter, we seek to construct the system that produces the data that we would like to observe, i.e., the desired behavior. Our approach allows us to exploit methods from Bayesian statistics, including efficient exploration of models spaces and high-dimensional parameter spaces, and the ability to rank models with respect to their ability to generate certain types of data. Bayesian model selection furthermore automatically strikes a balance between complexity and (predictive or explanatory) performance of mathematical models. To deal with the complexities of molecular systems we employ an approximate Bayesian computation scheme which only requires us to simulate from different competing models to arrive at rational criteria for choosing between them. We illustrate the advantages resulting from combining the design and modeling (or in silico prototyping) stages currently seen as separate in synthetic biology by reference to deterministic and stochastic model systems exhibiting adaptive and switch-like behavior, as well as bacterial two-component signaling systems.