It has been proposed that Mars' moons formed from a disk produced by a large impact with the planet. However, whether such an event could produce tiny Phobos and Deimos remains unclear. Using a hybrid N-body model of moon accumulation that includes a full treatment of moon-moon dynamical interactions, we first identify new constraints on the disk properties needed to produce Phobos and Deimos. We then simulate the impact formation of disks using smoothed particle hydrodynamics, including a novel approach that resolves the impact ejecta with order-of-magnitude finer mass resolution than existing methods. We find that forming Phobos-Deimos requires an oblique impact by a Vesta-to-Ceres sized object with ∼10-3 times Mars' mass, a much less massive impactor than previously considered.