In the late 1800s, G.K. Gilbert provided the first stratigraphic description of river delta deposits, but later work revealed that the “Gilbert-type” model, long thought to be universal, did not apply to all deltas. Here we propose that, in addition to “Gilbert-type” deltas (herein called foreset-dominated), there is a class of deltas with a basic, first-order stratigraphy that is topset-dominated. We develop a geometric model that predicts the occurrence of each delta type by calculating the topset and foreset thicknesses under different fluvial and basinal conditions. Our model predicts that topset-dominated deltas have a novel characteristic: their distributary channels commonly incise into pre-delta sediment. This type of delta should be common on shelves where the slope is less than ∼0.05° and the river feeding the delta has a discharge greater than ∼200 m3/s. Field data from Gulf of Mexico deltas confirm the prediction that distributary channels often incise into pre-delta sediment. Finally, we propose a new stratigraphic model for topset-dominated deltas and suggest that future stratigraphic interpretation must distinguish between delta types because the cause of channel incision for each is different and may be unrelated to allogenic changes.