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Abstract. Direct observations of the size of the Greenland Ice Sheet during Quaternary interglaciations are sparse yet valuable for testing numerical models of ice-sheet history and sea level contribution. Recent measurements of cosmogenicnuclides in bedrock from beneath the Greenland Ice Sheet collected duringpast deep-drilling campaigns reveal that the ice sheet was significantlysmaller, and perhaps largely absent, sometime during the past 1.1 millionyears. These discoveries from decades-old basal samples motivate new,targeted sampling for cosmogenic-nuclide analysis beneath the ice sheet.Current drills available for retrieving bed material from the US IceDrilling Program require < 700 m ice thickness and a frozen bed,while quartz-bearing bedrock lithologies are required for measuring a largesuite of cosmogenic nuclides. We find that these and other requirementsyield only ∼ 3.4 % of the Greenland Ice Sheet bed as asuitable drilling target using presently available technology. Additionalfactors related to scientific questions of interest are the following: which areas of thepresent ice sheet are the most sensitive to warming, where would a retreating icesheet expose bare ground rather than leave a remnant ice cap, andwhich areas are most likely to remain frozen bedded throughout glacialcycles and thus best preserve cosmogenic nuclides? Here we identifylocations beneath the Greenland Ice Sheet that are best suited for potentialfuture drilling and analysis. These include sites bordering Inglefield Landin northwestern Greenland, near Victoria Fjord and Mylius-Erichsen Land innorthern Greenland, and inland from the alpine topography along the icemargin in eastern and northeastern Greenland. Results from cosmogenic-nuclide analysis in new sub-ice bedrock cores from these areas would help to constrain dimensions of the Greenland Ice Sheet in the past.