Igneous sills can facilitate significant lateral magma transport in the crust; therefore, it is important to constrain controls on their formation and propagation. Close spatial association between sills and dikes in layered (sedimentary) host rocks has led to a number of sill emplacement mechanisms that involve stress rotation related to layering; from horizontal extension and dike emplacement, to horizontal compression and sill emplacement. Here, we used field observations in the San Rafael subvolcanic field (Utah, USA), on the Colorado Plateau, supported by mechanical modeling, to show that layering is not the dominant control in all cases of sill formation. We found no compelling evidence of large sills fed by dikes; all observed cases showed that either dikes cut sills, or vice versa. Local sill contacts activate and follow host layer interfaces, but regionally, sills cut the stratigraphy at a low angle. The sills cut and are cut by reverse faults (1–3 m displacement) and related fractures that accommodate horizontal shortening. Minor sill networks resemble extension vein meshes and indicate that horizontal and inclined geometries were formed during coaxial horizontal shortening and vertical thickening. Although sills elsewhere may be related to mechanical layering during tectonic quiescence, our mechanical models show that the observed San Rafael subvolcanic field geometries are favored in the upper crust during mild horizontal shortening. We propose that sill geometry provides an indication of regional stress states during emplacement, and not all sill geometry is a response to bedding. Constraining sill geometry may therefore present a useful tool in plate-tectonic studies.