The drainage of low-permeability unconventional reservoirs is often interpreted to be controlled by hydraulic and natural fractures that drain a homogenous low-permeability mudstone. However, stratigraphic heterogeneity, which results in strong variations in permeability, may also play an important role. We demonstrate that thin dolomitized carbonate sediment gravity flow deposits are over 25 times more permeable on average than the volumetrically dominant mudstone that is the source of most of the oil in the upper Wolfcamp interval of the Delaware Basin. We conducted steady-state liquid (dodecane) permeability measurements in 30 horizontal core plugs from six upper Wolfcamp lithofacies. The dolomitized calcareous lithofacies have effective permeabilities to dodecane of up to 2000 nd, whereas the remaining mudstones, dolomudstones, and calcite-bearing lithofacies have permeabilities of less than 60 nd. We constructed a layered flow model to examine the role of high-permeability layers in drainage at the completion scale. Flow is focused through the permeable layer, resulting in upscaled permeabilities and production rates that are up to four times greater than a reservoir composed of only low-permeability strata. Our analysis shows the importance of understanding stratigraphy, permeability, and flow behavior at the thin-bed scale. This understanding can illuminate what landing zones will be economical, the optimal spacing of hydraulic fractures, and whether there will be significant interference between multiple wells during production. The flow focusing that we infer from the Wolfcamp is most likely a universal characteristic of unconventional reservoirs.