Mosquito-borne alphaviruses, which replicate alternately and obligately in mosquitoes and vertebrates, appear to experience lower rates of evolution than do many RNA viruses that replicate solely in vertebrates. This genetic stability is hypothesized to result from the alternating host cycle, which constrains evolution by imposing compromise fitness solutions in each host. To test this hypothesis, Sindbis virus was passaged serially, either in one cell type to eliminate host alteration or alternately between vertebrate (BHK) and mosquito (C6/36) cells. Following 20 to 50 serial passages, mutations were identified and changes in fitness were assessed using competition assays against genetically marked, surrogate parent viruses. Specialized viruses passaged in a single cell exhibited more mutations and amino acid changes per passage than those passaged alternately. Single host-adapted viruses exhibited fitness gains in the cells in which they specialized but fitness losses in the bypassed cell type. Most but not all viruses passaged alternately experienced lesser fitness gains than specialized viruses, with fewer mutations per passage. Clonal populations derived from alternately passaged viruses also exhibited adaptation to both cell lines, indicating that polymorphic populations are not required for simultaneous fitness gains in vertebrate and mosquito cells. Nearly all passaged viruses acquired Arg or Lys substitutions in the E2 envelope glycoprotein, but enhanced binding was only detected for BHK cells. These results support the hypothesis that arbovirus evolution may be constrained by alternating host transmission cycles, but they indicate a surprising ability for simultaneous adaptation to highly divergent cell types by combinations of mutations in single genomes.