Considerable evidence now exists for high-frequency climate changes in the last ice age cycle (Dansgaard-Oeschger and Bond cycles). Though large-scale ice sheet flow has too long a time constant to play a significant role in these events, stochastically forced changes in the mass balance of the Pleistocene ice sheets may have resulted in significant variation in freshwater flux to the North Atlantic. In this paper we mimic the effects of natural climate variability with small (≤0.5W/m2) stochastic changes in insolation and examine the response in terms of ice volume change in an ensemble of coupled energy balance/ice sheet model runs. The total change in ice mass is comparable to a third of the volume of the current Greenland ice sheet, with meltwater discharge potentially sufficient to trigger Dansgaard-Oeschger type events. In general, the Eurasian ice sheet is more sensitive to perturbations than the North American ice sheet. The distribution and occurrence of spectral peaks in the 1--9 kyr band is also comparable to the record of millennial oscillations over the last 500,000 years in a subpolar North Atlantic core. Our results suggest that considerable caution is necessary in interpreting the physical significance of sub-Milankovitch spectral peaks in paleo time series.