In this paper, we summarize the issues that should be considered when designing broadband quasioptical systems for submillimetre-wave radioastronomy receivers. We cover topics such as bandwidth, cross-talk, truncation, and aberrations, and we argue that it should be possible to manufacture high-efficiency systems that have several octaves of bandwidth. A key feature of the paper is that we use the language of multimode Gaussian optics throughout, and in this way, we emphasize that a receiver is a diffraction-limited imaging system rather than just a collection of components for guiding Gaussian beams. The whole discussion is conducted in terms of a particular system we are constructing for the James Clerk Maxwell Telescope in Hawaii.