Tumor evolution is an iterative process of selection for pro-oncogenic aberrations. This process can be accelerated by genomic instability, but how it interacts with different selection bottlenecks to shape the evolving genomic landscape remains understudied. Here, we assessed tumor initiation and therapy resistance bottlenecks in mouse models of melanoma, with or without genomic instability. At the initiation bottleneck, whole-exome sequencing revealed that drug-naive tumors were genomically silent, and this was surprisingly unaffected when genomic instability was introduced via telomerase inactivation. We hypothesize that the strong engineered alleles created low selection pressure. At the therapy resistance bottleneck, strong selective pressure was applied using a BRAF inhibitor. In the absence of genomic instability, tumors acquired a non-genomic drug resistance mechanism. By contrast, telomerase-deficient, drug-resistant melanomas acquired highly recurrent copy number gains. These proof-of-principle experiments demonstrate how different selection pressures can interact with genomic instability to impact tumor evolution.