Analysis of the Vostok ice-core record of 10Be (Raisbeck et al. 1987) suggests that the sharply resolved increases in 10Be at 35 ka (kyr) and 60 ka are due to cosmic-ray (CR) increases. As an alternate to long-term solar modulation or strong decreases in the Earth's magnetic field, supernova (SN) forcing is qualitatively consistent with the generation of a forward-reverse shock ensemble from a spherical blast wave of age very approximately at 75 ka. This age agrees with Davelaar, Bleeker and Deerenberg's (1980) identification of 75 ka for the age of a North Polar Spur SN remnant. Confirmation would be the first geochemical detection of supernova forcing of spallogenic and perhaps cosmogenic isotope production in the atmosphere. The three 10Be increases can be satisfied by a modification of the Sonett, Morfill, and Jokipii (1987) model. This consists of 2 or 3 shock waves from a single SN event, which includes the first stage in the expansion, leading to a forward shock, S1+, and a pair of reverse waves, S1− and S2−. One reverse wave arises from the spherical expansion, itself, and the other is a reflected wave from a remnant precursor shell boundary from a more ancient SN. The model requires the solar system to be immersed in the ‘bubble’ of the earlier post-SN evolution, possibly affecting estimates of heliospheric boundary distance. However more recent analysis of Camp Century ice core data discloses only the 35 ka 10Be peak. This recent result compounds the difficulty of constructing a completely consistent model for the source of the Vostok spikes. This paper is written in the spirit of suggesting only one of possibly several different models, even within the subclass of SN models.