The authors present a technique for determining the power that is lost when the field in a beam waveguide is truncated by an axially-symmetric stop. The technique is based on the principles of multimode Gaussian optics. Although the underlying theory is applicable to any long-focal-length optical system, they concentrate on beam waveguides that are fed by diagonal horns, corrugated horns, smooth-walled conical horns, and uniformly-illuminated apertures. The results are summarized in a series of plots which show truncation loss as a function of normalised aperture size and phase slippage. These plots can be used together with single-mode design techniques to minimize the size of millimeter and submillimeter-wave optical systems