We present a method for estimating the distribution of fitness effects of new amino acid mutations when those mutations can be assumed to be slightly advantageous, slightly deleterious, or strongly deleterious. We apply the method to mitochondrial data from several different species. In the majority of the data sets, the shape of the distribution is approximately exponential. Our results provide an estimate of the distribution of fitness effects of weakly selected mutations and provide a possible explanation for why the molecular clock is fairly constant across taxa and time.