The formation of monolayer and multilayer ice with a square lattice structure has recently been reported on the basis of transmission electron microscopy experiments, renewing interest in confined two-dimensional ice. Here we report a systematic density functional theory study of double-layer ice in nanoconfinement. A phase diagram as a function of confinement width and lateral pressure is presented. Included in the phase diagram are honeycomb hexagonal, square-tube, hexagonal-close-packed, and buckled-rhombic structures. However, contrary to experimental observations, square structures do not feature: our most stable double-layer square structure is predicted to be metastable. This study provides general insight into the phase transitions of double-layer confined ice and a fresh theoretical perspective on the stability of square ice in graphene nanocapillary experiments.