We have constructed and compared high peak power YAG-pumped dye lasers using a variety of beam expansion methods, particularly the Cassegrainian telescope, grazing-incidence, and achromaticprism beam expander designs. We find that the Cassegrainian design offers a modest advantage over the conventional Hänsch or refractive telescope design in larger magnification and hence, narrower linewidth, while retaining several inherent drawbacks in cost, alignment difficulty, and amplified spontaneous emission (ASE) problems. New problems specific to the Cassegrainian design in high-power operation include limited wavelength range of the telescope secondary and a severe diffraction grating damage mechanism during alignment. We conclude that, on the whole, the Hänsch and Cassegrainian designs offer roughly equal performance. By comparison, the grazing-incidence design offers significant advantages in cost, ease of alignment, and linewidth without an etalon, but with reductions in efficiency, power output, and in some cases, wavelength stability. Our final judgment is that for high-power multimode operation, the four-prism achromatic beam expander is generally superior to the other designs. For single-mode operation, however, the prism design is rivaled by several ingenious grazing-incidence variations.