A new method is proposed for inferring topology for evolutionary trees. Existing methods have complementary strengths and weaknesses. Maximum and transversion parsimony are powerful methods, but they lack statistical consistency, that is, they do not always infer the correct tree as the sequence length becomes very large. Evolutionary parsimony overcomes this deficiency, but it may lack sufficient power when sequence length is small (less than 1000 aligned nucleotides; Sinsheimer, Lake, and Little, 1996, Biometrics 52, 193-210). Our proposed method, evolutionary-symmetric transversion parsimony, is a hybrid that retains the consistency of evolutionary parsimony, while increasing power by incorporating a modified form of transversion parsimony within a statistical model. The method requires choice of a parameter $gamma$ that represents the prior probability that symmetric transversion parsimony yields consistent results. Properties of the method are assessed for a variety of choices of $gamma$ in a large simulation study. In general, inference under the evolutionary-symmetric transversion parsimony has more discriminating power than inference under evolutionary parsimony and is better calibrated than inference under symmetric transversion parsimony. The results are quite robust to the choice of $gamma$, indicating a value of 0.90 as a reasonable overall choice when the true value of $gamma$ ranges between 0.85 to 1.00. Our method is, like evolutionary parsimony and maximum parsimony, computationally straightforward. The same statistical approach can be applied to combine evolutionary parsimony with other inconsistent methods, such as maximum parsimony, but at the expense of more difficult computations.