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Three optimality criteria for convolutional codes are considered in this correspondence: namely, free distance, minimum distance, and distance profile. Here we report the results of computer searches for rate one-half binary convolutional codes that are "robustly optimal" in the sense of being optimal for one criterion and optimal or near-optimal for the other two criteria. Comparisons with previously known codes are made. The results of a computer simulation are reported to show the importance of the distance profile to computational performance with sequential decoding.