Climate-controlled changes in eustatic sea level (ESL) are linked to transfers of water between ocean and land, thus offering a rare insight into the past hydrological cycle. In this study, we examine the timing and phase of Milankovitch-scale ESL cycles in the peak Cretaceous greenhouse, the early Turonian (-93-94 million years, Myr, ago). A high-resolution astronomical framework established for the Bohemian Cretaceous Basin (central Europe) suggests a -400-kyr pace and a distinct asymmetry of interpreted ESL cycles. The rising limbs of ESL change constitute only 20-30 % of the cycle, and are encased entirely within the falling phase of the 405-kyr eccentricity. The intervening ESL falls (<= 6 m in magnitude) are more protracted, starting within 70 kyr prior to the eccentricity minima and culminating -60 kyr after the 405-kyr eccentricity maxima. Despite similarities to the sawtooth shape of -100-kyr glacioeustatic oscillations of the Late Pleistocene, the time scales and phasing are unparalleled in the Pleistocene icehouse. A similar, 405-kyr pace is found in ice-volume variations of the early Miocene, but the timing of glacioeustatic change relative to eccentricity forcing is incompatible with the phase of greenhouse sea-level oscillations. The phasing points to major differences in the geographic location and insolation sensitivity of the key hydrological reservoirs under icehouse and greenhouse regimes. The inferred structure of greenhouse eustasy points to low- or middle-latitude water storage, likely aquifers, that charge (expand) with rising seasonality variations and discharge (contract) with declining seasonality amplitudes on the 405-kyr scale. The net volume of water transferred on these time scales is within 2.2 x 106 km3, equivalent to <= 10 % of the present-day storage in the uppermost 2 km of continental crust. Potential additive interference with steric eustasy, proportionally relevant during greenhouse regimes, could reduce the volumes required for continental storage.