Recent experiments have indicated that Josephson-junction arrays can radiate coherently in a laser-like fashion, as predicted by theoretical work in the 1970s. We present results from measurements of high-efficiency Josephson-junction arrays coupled to resonant cavities. In one of our samples with four columns and 36 rows, the dc to ac (180 GHz) conversion efficiency reaches an asymptotic value of about 32%. Using a simple circuit model we show that we have achieved optimal dc to ac conversion in this sample. (C) 2001 American Institute of Physics.