RNA viruses pose serious threats to human health. Their success relies on their capacity to generate genetic variability and, consequently, on their adaptive potential. We describe a strategy to attenuate RNA viruses by altering their evolutionary potential. We rationally altered the genomes of Coxsackie B3 and influenza A viruses to redirect their evolutionary trajectories towards detrimental regions in sequence space. Specifically, viral genomes were engineered to harbour more serine and leucine codons with nonsense mutation targets: codons that could generate Stop mutations after a single nucleotide substitution. Indeed, these viruses generated more Stop mutations both in vitro and in vivo, accompanied by significant losses in viral fitness. In vivo, the viruses were attenuated, generated high levels of neutralizing antibodies and protected against lethal challenge. Our study demonstrates that cornering viruses in 'risky' areas of sequence space may be implemented as a broad-spectrum vaccine strategy against RNA viruses.