Systematic mappings of the effects of protein mutations are becoming increasingly popular. Unexpectedly, these experiments often find that proteins are tolerant to most amino acid substitutions, including substitutions in positions that are highly conserved in nature. To obtain a more realistic distribution of the effects of protein mutations, we applied a laboratory drift comprising 17 rounds of random mutagenesis and selection of M.HaeIII, a DNA methyltransferase. During this drift, multiple mutations gradually accumulated. Deep sequencing of the drifted gene ensembles allowed determination of the relative effects of all possible single nucleotide mutations. Despite being averaged across many different genetic backgrounds, about 67% of all nonsynonymous, missense mutations were evidently deleterious, and an additional 16% were likely to be deleterious. In the early generations, the frequency of most deleterious mutations remained high. However, by the 17th generation, their frequency was consistently reduced, and those remaining were accepted alongside compensatory mutations. The tolerance to mutations measured in this laboratory drift correlated with sequence exchanges seen in M.HaeIII's natural orthologs. The biophysical constraints dictating purging in nature and in this laboratory drift also seemed to overlap. Our experiment therefore provides an improved method for measuring the effects of protein mutations that more closely replicates the natural evolutionary forces, and thereby a more realistic view of the mutational space of proteins.