We present a new and more efficient method of calculating the losses of a waveguide laser resonator consisting of a hollow circular dielectric waveguide and flat mirrors, taking into account the effects of waveguide modes up to order HE13. Both symmetric and asymmetric cavities are considered. We show that low cavity losses, only slightly exceeding the HE11waveguiding losses, are predicted to be possible for much larger mirror distances than had previously been suspected, provided that an optimum total cavity length is chosen. The low losses arise when the HE11and HE12modes emerge from the guide with relative amplitudes and phases such that the returning diffraction patterns interfere to produce a narrow beam with low aperture losses. The theoretical predictions were checked experimentally for CO2lasers having various waveguide dimensions. Good qualitative agreement was found, but the optimum total cavity lengths were typically 3-5 percent longer than predicted. Possible explanations of this discrepancy are discussed. We also predicted and experimentally verified that variations of the cavity length over a few centimeters can exert a coarse wavelength selectivity sufficient to determine the band and branch on which a CO2laser oscillates; conversely, that for a grating tuned laser, the cavity length must be varied by a similar amount as the wavelength is tuned in order to maintain low cavity losses over the entire wavelength range.