In view of the increasing importance of nanoconfined aqueous solutions for various technological applications, it has become necessary to understand how strong confinement affects the properties of water at the level of molecular and even electronic structure. By performing extensive ab initio simulations of two-dimensionally nanoconfined water lamellae between graphene sheets subject to different interlayer spacings, we find new regimes at interlayer distances of 10 Å and less where water can be described neither to behave like interfacial water nor to be bulklike at the level of its H-bonding characteristics and electronic structure properties. It is expected that this finding will offer new opportunities to tune both diffusive and reactive processes taking place in aqueous environments that are strongly confined by chemically inert hard walls.