It is clear from multiple modeling and field studies that deltas can attain a shelf-edge position under conditions of rising sea level, and this is accepted as an alternative way to form submarine fans without relative sea-level lowstand conditions. However, the relative importance and the range of controls that generate this type of shelf-edge deltas are less well known. To investigate these controls, we input the natural range of seven accommodation and morphological variables to a geometric model that estimates the required sediment load to form the highstand shelf-edge delta. We conduct a one-at-a-time sensitivity analysis on each variable to determine their relative importance. Our results suggest that, other than sediment supply, shelf width is the most important control in forcing deltas to the shelf edge during rising sea level. Two of the traditional stratigraphic trinity, i.e., eustatic sea-level change and shelf subsidence, most likely play less important roles than implied in the literature. This result is consistent with a recent trend in sequence stratigraphic studies encouraging consideration of multiple controls in all interpretations, rather than assuming dominant control by relative sea level.