Background: In mammals, contrary to what is usually assumed, recent evidence suggests that synonymous mutations may not be selectively neutral. This position has proven contentious, not least because of the absence of a viable mechanism. Here we test whether synonymous mutations might be under selection owing to their effects on the thermodynamic stability of mRNA, mediated by changes in secondary structure. Results: We provide numerous lines of evidence that are all consistent with the above hypothesis. Most notably, by simulating evolution and reallocating the substitutions observed in the mouse lineage, we show that the location of synonymous mutations is non-random with respect to stability. Importantly, the preference for cytosine at 4-fold degenerate sites, diagnostic of selection, can be explained by its effect on mRNA stability. Likewise, by interchanging synonymous codons, we find naturally occurring mRNAs to be more stable than simulant transcripts. Housekeeping genes, whose proteins are under strong purifying selection, are also under the greatest pressure to maintain stability. Conclusion: Taken together, our results provide evidence that, in mammals, synonymous sites do not evolve neutrally, at least in part owing to selection on mRNA stability. This has implications for the application of synonymous divergence in estimating the mutation rate.