We analyze how lethal mutagenesis operates in a compartmentalized host. We assume that different compartments receive different amounts of mutagen and that virions can migrate among compartments. We address two main questions: (1) To what extent can refugia, i.e., compartments that receive little mutagen, prevent extinction? (2) Does migration among compartments limit the effectiveness of refugia? We find that if there is little migration, extinction has to be achieved separately in all compartments. In this case, the total dose of mutagen administered to the host needs to be so high that the mutagen is effective even in the refugia. By contrast, if migration is extensive, then lethal mutagenesis is effective as long as the average growth in all compartments is reduced to below replacement levels. The effectiveness of migration is governed by the ratio of virion replication and death rates, R(0). The smaller R(0), the less migration is necessary to neutralize refugia and the less mutagen is necessary to achieve extinction at high migration rates.