The genetic architecture of many phenotypic traits is such that genes often contribute to multiple traits, and mutations in these genes can therefore affect multiple phenotypes. These pleiotropic interactions often manifest as tradeoffs between traits where improvement in one property entails a cost in another. The life cycles of many pathogens include periods of growth within a host punctuated with transmission events, such as passage through a digestive tract or a passive stage of exposure in the environment. Populations exposed to such fluctuating selective pressures are expected to acquire mutations showing tradeoffs between reproduction within and survival outside of a host. We selected for individual mutations under fluctuating selective pressures for a ssDNA microvirid bacteriophage by alternating selection for increased growth rate with selection on biophysical properties of the phage capsid in high-temperature or low-pH conditions. Surprisingly, none of the seven unique mutations identified showed a pleiotropic cost; they all improved both growth rate and pH or temperature stability, suggesting that single mutations even in a simple genetic system can simultaneously improve two distinct traits. Selection on growth rate alone revealed tradeoffs, but some mutations still benefited both traits. Tradeoffs were therefore prevalent when selection acted on a single trait, but payoffs resulted when multiple traits were selected for simultaneously. We employed a molecular-dynamics simulation method to determine the mechanisms underlying beneficial effects for three heat-shock mutations. All three mutations significantly enhanced the affinities of protein-protein interfacial bindings, thereby improving capsid stability. The ancestral residues at the mutation sites did not contribute to protein-protein interfacial binding, indicating that these sites acquired a new function. Computational models, such as those used here, may be used in future work not only as predictive tools for mutational effects on protein stability but, ultimately, for evolution.