Prestrained elastic sheets are thin structures in which the ground state is not a rigid motion, but is instead characterized by a preferred metric varying with position. Such prestrain can be caused by adding inclusions to an already existing sheet, or by heating a sheet that is built to swell differentially throughout; it is also thought to occur by natural growth. Energy minimization drives such a sheet to deform into exotic configurations. In this talk, we explore the link between the regularity of the prestrain and the minimum energy. An upper bound on the energy can be derived in terms of the regularity of the prestrain; a lower bound follows from known irregularities. The bounds match up to corrections that seem to require finer details of the prestrain. This is joint work with Ian Tobasco.