Ice thickness in West Antarctica at the Last Glacial Maximum (LGM) is poorly known, yet is key information for understanding ice streams and interpreting ice cores. Although trim lines, moraine limits, and exposure-age dating provide geologic constraints on ice thickness near the Transantarctic Mountains and in Marie Byrd Land, lack of exposed bedrock hampers traditional geologic methods in a central, ∼2 × 106 km2 region. Here we infer ice-sheet thickness changes in the central Ross Sea Embayment by using a transient ice-flow model to find combinations of accumulation-rate and ice-sheet thickness histories that match the depth-age relationship and the measured layer-thickness pattern in the Siple Dome ice core. After we reject unreasonable accumulation-rate histories, the remaining history pairs indicate thinning of 200–400 m since the LGM. Our estimate is lower than previous reconstructions that were constrained by geologic evidence from the Transantarctic Mountains and by marine data from the Ross Sea floor, which indicate that a grounded ice sheet extended to the continental shelf margin during the last glacial period. Low surface elevations in the central Ross Sea Embayment during the LGM do not preclude thicker ice along its boundaries. However, if this grounded ice sheet came over 1000 km from interior West Antarctica, as is usually assumed, then it had very low surface slope, requiring a very slippery bed. Alternatively, the grounded Ross Sea ice might have flowed from the Transantarctic Mountains and western Marie Byrd Land.