The modes of geologic storage of CO2 are usually categorized as structural, dissolution, residual, and mineral trapping. Here we argue that the heterogeneity intrinsic to sedimentary rocks gives rise to a fifth category of storage, which we call local capillary trapping. Local capillary trapping occurs during buoyancy-driven migration of bulk phase CO2 within a saline aquifer. When the rising CO2 plume encounters a region (10(-2) to 10(+1)m) where capillary entry pressure is locally larger than average, CO2 accumulates beneath the region. This form of storage differs from structural trapping in that much of the accumulated saturation will not escape, should the integrity of the seal overlying the aquifer be compromised. Local capillary trapping differs from residual trapping in that the accumulated saturation can be much larger than the residual saturation for the rock. We examine local capillary trapping in a series of numerical simulations. The essential feature is that the drainage curves (capillary pressure versus saturation for CO2 displacing brine) are required to be consistent with permeabilities in a heterogeneous domain. In this work, we accomplish this with the Leverett J-function, so that each grid block has its own drainage curve, scaled from a reference curve to the permeability and porosity in that block. We find that capillary heterogeneity controls the path taken by rising CO2. The displacement front is much more ramified than in a homogeneous domain, or in a heterogeneous domain with a single drainage curve. Consequently, residual trapping is overestimated in simulations that ignore capillary heterogeneity. In the cases studied here, the reduction in residual trapping is compensated by local capillary trapping, which yields larger saturations held in a smaller volume of pore space. Moreover, the amount of CO2 phase remaining mobile after a leak develops in the caprock is smaller. Therefore, the extent of immobilization in a heterogeneous formation exceeds that reported in previous studies of buoyancy-driven plume movement.