Mutation rates and fitness effects are often treated as independent, but mutation rates are variable and evolve under indirect selection. For example, human European populations experienced a transient increase in the 3-mer mutation rate TCC -> TTC in the past 20,000 years. To quantify indirect selection on mutation spectra, we developed an approach to estimate the distribution of fitness effects (DFE) of nonsynonymous 3-mer mutation types, by analyzing pairs of inverse mutation types to account for GC-biased gene conversion and ancestral state misidentification. We then applied this approach to all 96 possible 3-mer mutation types in humans, using data from the 1000 Genomes Project. We found widely varying DFEs among mutation types that are strongly correlated with amino acid exchangabilities. Our DFE estimate for TCC -> TTC mutations is consistent with recent theoretical predictions by Milligan, Amster, and Sella of scenarios under which a moderate number of modifier loci could yield population-specific transient bursts of a specific mutation type. More broadly, we find evidence for fine-tuning of the human mutation spectrum to reduce deleterious mutation effects.