The North Atlantic sediment record suggests quasi-periodic (7000- to 12,000-year period) ice-rafted debris (IRD) depositions during at least the last glacial period. The cause of these Heinrich events, as they are commonly known, is not fully understood; however, they may point to surges of the ice stream that drained the Hudson Bay/Hudson Strait region of the Laurentide Ice Sheet. We investigate a simple conceptual model of ice stream instability (the binge/purge model) to suggest ways in which the ice stream could have entrained sufficient debris to account for the estimated mass of IRD associated with a typical Heinrich IRD layer in the North Atlantic (1.0 ± 0.3 × 1015 kg). We find that freezing of debris-laden ice at the bed of the ice stream during the brief (≈ 750 years) surge phase of the ice stream's hypothesized binge/purge cycle can incorporate up to 5.1 × 1015 kg. This amount is sufficient to meet the constraints of the North Atlantic sediment record but by no means verifies the binge/purge model as the cause of Heinrich events.