Like other arthropod-borne viruses (arboviruses), mosquito-borne dengue virus (DENV) is maintained in an alternating cycle of replication in arthropod and vertebrate hosts. The trade-off hypothesis suggests that this alternation constrains DENV evolution because a fitness increase in one host usually diminishes fitness in the other. Moreover, the hypothesis predicts that releasing DENV from host alternation should facilitate adaptation. To test this prediction, DENV was serially passaged in either a single human cell line (Huh-7), a single mosquito cell line (C6/36), or in alternating passages between Huh-7 and C6/36 cells. After 10 passages, consensus mutations were identified and fitness was assayed by evaluating replication kinetics in both cell types as well as in a novel cell type (Vero) that was not utilized in any of the passage series. Viruses allowed to specialize in single host cell types exhibited fitness gains in the cell type in which they were passaged, but fitness losses in the bypassed cell type, and most alternating passages, exhibited fitness gains in both cell types. Interestingly, fitness gains were observed in the alternately passaged, cloned viruses, an observation that may be attributed to the acquisition of both host cell-specific and amphi-cell-specific adaptations or to recovery from the fitness losses due to the genetic bottleneck of biological cloning. Amino acid changes common to both passage series suggested convergent evolution to replication in cell culture via positive selection. However, intriguingly, mutations accumulated more rapidly in viruses passed in Huh-7 cells than in those passed in C6/36 cells or in alternation. These results support the hypothesis that releasing DENV from host alternation facilitates adaptation, but there is limited support for the hypothesis that such alternation necessitates a fitness trade-off. Moreover, these findings suggest that patterns of genetic evolution may differ between viruses replicating in mammalian and mosquito cells.