Currently, major efforts are under way to refine the horizontal resolution of weather and climate models to kilometer-scale grid spacing (Δx). Besides refining the representation of the atmospheric dynamics and enabling the use of explicit convection, this will also provide higher resolution in the representation of orography. This study investigates the influence of these resolution increments on the simulation of orographic moist convection. Nine days of fair-weather thermally driven flow over the Alps are analyzed. Two sets of simulations with the COSMO model are compared, each consisting of three runs at Δx of 4.4, 2.2, and 1.1 km: one set using a fixed representation of orography at a resolution of 8.8 km, and one with varying representation at the resolution of the computational mesh. The spatial distribution of precipitation during daytime is only marginally affected by the orographic details, but nighttime convection to the south of the Alps—triggered by cold-air outflow from the valleys—is very sensitive to orography and precipitation is enhanced if more detailed orography is provided. During daytime, the onset of precipitation is delayed. The amplitude of the diurnal cycle of precipitation is reduced, even though more moisture converges toward the Alpine region during the afternoon. The hereby accumulated moisture sustains precipitation during the evening and nighttime over the surrounding plains. For these differences, the effects of changes in orographic detail are more important than changes in grid spacing. In addition, the individual convective cells are weaker, but their number increases with higher resolved orography.