The prospect of utilizing CRISPR-based gene-drive technology for controlling populations has generated much excitement. However, the potential for spillovers of gene-drive alleles from the target population to non-target populations has raised concerns. Here, using mathematical models, we investigate the possibility of limiting spillovers to non-target populations by designing differential-targeting gene drives, in which the expected equilibrium gene-drive allele frequencies are high in the target population but low in the non-target population. We find that achieving differential targeting is possible with certain configurations of gene-drive parameters, but, in most cases, only under relatively low migration rates between populations. Under high migration, differential targeting is possible only in a narrow region of the parameter space. Because fixation of the gene drive in the non-target population could severely disrupt ecosystems, we outline possible ways to avoid this outcome. We apply our model to two potential applications of gene drives-field trials for malaria-vector gene drives and control of invasive species on islands. We discuss theoretical predictions of key requirements for differential targeting and their practical implications.