We investigate three-flat calibration methods based on rotational symmetry and mirror symmetry for absolute interferometric flatness measurements of circular flats in the presence of deformations caused by the support mechanism for the flats, which are a significant problem for large, heavy flats. We show that the mirror-symmetric component of the mounting-induced deformation can be determined by comparing flat test solutions based on mirror symmetry and on rotational symmetry, when the flats have identical deformations. We also describe a novel solution to the three-flat problem for three flats with identical mounting-induced deformations. In the new three-flat solution, the flat deformation is calculated along with the wavefront flatness errors for the three flats. Formulas for the uncertainty of three-flat test solutions are derived.