We demonstrate an algorithm for computing local coupled-cluster doubles (LCCD) energies that form rigorously smooth potential-energy surfaces and which should be fast enough for application to large systems in the future. Like previous LCCD algorithms, our method solves iteratively for only a limited number of correlation amplitudes, treating the remaining amplitudes with second-order perturbation theory. However, by employing bump functions, our method smoothes the transition from iteratively solved amplitude to perturbation-treated amplitude, invoking the implicit function theorem to prove that our LCCD energy is an infinitely differentiable function of nuclear coordinates. We make no explicit amplitude domains nor do we rely on the existence of atom-centered, redundant orbitals in order to get smooth potential-energy curves. In fact, our algorithm employs only localized orthonormal occupied and virtual orbitals. Our approach should be applicable to many other electron correlation methods.