Abstract: An approach is presented to experimentally constrain previously unreachable (p,gamma) reaction rates on nuclei far from stability in the astrophysical rp process. Energies of all critical resonances in the Cu-57(p,gamma)Zn-58 reaction are deduced by populating states in Zn-58 with a (d, n) reaction in inverse kinematics at 75 MeV/u, and detecting.-ray-recoil coincidences with the state-of-the-art gamma-ray tracking array GRETINA and the S800 spectrograph at the National Superconducting Cyclotron Laboratory. The results reduce the uncertainty in the Cu-57(p,gamma) reaction rate by several orders of magnitude. The effective lifetime of Ni-56, an important waiting point in the rp process in x-ray bursts, can now be determined entirely from experimentally constrained reaction rates.