The long-standing view of Earth's Cenozoic glacial history calls for the first continental-scale glaciation of Antarctica in the earliest Oligocene epoch ( approximately 33.6 million years ago), followed by the onset of northern-hemispheric glacial cycles in the late Pliocene epoch, about 31 million years later. The pivotal early Oligocene event is characterized by a rapid shift of 1.5 parts per thousand in deep-sea benthic oxygen-isotope values (Oi-1) within a few hundred thousand years, reflecting a combination of terrestrial ice growth and deep-sea cooling. The apparent absence of contemporaneous cooling in deep-sea Mg/Ca records, however, has been argued to reflect the growth of more ice than can be accommodated on Antarctica; this, combined with new evidence of continental cooling and ice-rafted debris in the Northern Hemisphere during this period, raises the possibility that Oi-1 represents a precursory bipolar glaciation. Here we test this hypothesis using an isotope-capable global climate/ice-sheet model that accommodates both the long-term decline of Cenozoic atmospheric CO(2) levels and the effects of orbital forcing. We show that the CO(2) threshold below which glaciation occurs in the Northern Hemisphere ( approximately 280 p.p.m.v.) is much lower than that for Antarctica ( approximately 750 p.p.m.v.). Therefore, the growth of ice sheets in the Northern Hemisphere immediately following Antarctic glaciation would have required rapid CO(2) drawdown within the Oi-1 timeframe, to levels lower than those estimated by geochemical proxies and carbon-cycle models. Instead of bipolar glaciation, we find that Oi-1 is best explained by Antarctic glaciation alone, combined with deep-sea cooling of up to 4 degrees C and Antarctic ice that is less isotopically depleted (-30 to -35 per thousand) than previously suggested. Proxy CO(2) estimates remain above our model's northern-hemispheric glaciation threshold of approximately 280 p.p.m.v. until approximately 25 Myr ago, but have been near or below that level ever since. This implies that episodic northern-hemispheric ice sheets have been possible some 20 million years earlier than currently assumed (although still much later than Oi-1) and could explain some of the variability in Miocene sea-level records.