The projected contribution to sea-level rise from the Greenland Ice Sheet currently has a large spread in literature, ranging from about 14 to 255 mm by the year 2100. Part of this spread is due to uncertainty in mass loss from ocean-terminating outlet glaciers in response to terminus retreat. Here, we use a diffusive-kinematic wave formulation of glacier thinning to show that steep bed features can limit thinning from diffusing inland from a glacier’s terminus. This simplified model allows us to rank 141 of Greenland’s outlet glaciers based on their potential to allow thinning to diffuse far inland and, thus, contribute to sea-level rise over the next century. We then target two glaciers: Kakivfaat Sermiat (KAK) in West Greenland and Kangerlussuaq Gletscher (KLG) in East Greenland. Both glaciers have a high potential to contribute to sea-level rise but with contrasting bed geometries; KAK has relatively low ice flux but its geometry can allow thinning to diffuse far inland while KLG has high ice flux but a geometry that will limit thinning to 30 km inland of its terminus. We simulate mass loss from each glacier, in response to prescribed terminus retreat, using a higher-order numerical model, and find very different response times of mass loss from the two glaciers over the next century. KLG reaches a new steady state by 2100, while the slow inland diffusion of thinning causes KAK to continue its response into the next century and beyond. As a result, KAK contributes nearly twice the volume of ice to sea-level rise of KLG by year 2200, suggesting that low-flux glaciers that can allow thinning to spread far into the ice sheet interior may contribute much to sea-level rise as high-flux glaciers that limit thinning to their lowest reaches. By identifying the glaciers around the ice sheet with the highest potential to contribute to sea-level rise, we hope to help focus future higher-order numerical modeling studies working toward narrowing the range in sea-level rise projections.