© 2017 Society of Photo-Optical Instrumentation Engineers (SPIE). Achieving high-throughput extreme ultraviolet (EUV) patterning remains a major challenge due to low source power; phase-shift masks can help solve this challenge for dense features near the resolution limit by creating brighter images than traditional absorber masks when illuminated with the same source power. We explore applications of etched multilayer phase-shift masks for EUV lithography, both in the current-generation 0.33 NA and next-generation 0.55 NA systems. We derive analytic formulas for the thin-mask throughput gains, which are 2.42× for lines and spaces and 5.86× for contacts compared with an absorber mask with dipole and quadrupole illumination, respectively. Using rigorous finite-difference time-domain simulations, we quantify variations in these gains by pitch and orientation, finding 87% to 113% of the thin-mask value for lines and spaces and a 91% to 99% for contacts. We introduce an edge placement error metric, which accounts for CD errors, relative feature motion, and telecentricity errors, and use this metric both to optimize mask designs for individual features and to explore which features can be printed on the same mask. Furthermore, we find that although partial coherence shrinks the process window, at an achievable sigma of 0.2 we obtain a depth of focus of 340 nm and an exposure latitude of 39.2%, suggesting that partial coherence will not limit the feasibility of this technology. Finally, we show that many problems such as sensitivity to etch uniformity can be greatly mitigated using a central obscuration in the imaging pupil.