A graded-reflectivity-mirror (GRM) unstable resonator with low output coupling is described, where a custom-made optical phase element is used inside the resonator to provide maximally flat output. The phase element removes the dip in the output beam by pre-compensating the internal Gaussian mode. An experiment is performed with a flashlamp-pumped Nd:YAG laser. The resonator's magnification (M) and the GRM's central reflectivity (Ro) are 2.3 and 0.7, respectively. The large dip in the center of the output is removed using the custom-made phase element. This resonator has the advantage over a conventional GRM unstable resonator of being suitable for lower-gain laser media. The gain required to overcome fundamental mode cavity losses for maximally flat output is decreased from 22.3 (for a conventional GRM resonator) to 4.3 (for the resonator containing the phase element). This reduction in required gain comes with essentially no loss to the resonator modal discrimination.