Very good imaging performance can be achieved in telescopes with fast parabolic primaries, with the aid of two-mirror correctors. We give details of a Paul-Baker type corrector for an f/l primary, relaying to an f/2 final focus. Images with 80% of the energy into 0.2 arc second diameter, or better, are obtained over a field of 10 diameter. The mechanical structure and enclosure of a large telescope built with these fast optics would be considerably smaller and less expensive than those for conventional optics. We explore an MMT design in which six off-axis primaries in a circle together form a Parabolic f/l surface. Other applications are in ultraviolet astronomy, where the high resolution with no refractive elements to give chromatic aberration is an advantage, and in infrared astronomy, where an off-axis part of the f/l parent gives a wide field telescope of very low emissivity. We also consider the use of the correctors for telescopes in which the aperture is a long thin rectangle, of fast focal ratio in its long dimension. This configuration has special advantages for diffraction limited imaging and interferometrv. Such telescopes can be as efficient for spectroscopy and photometry as circular mirrors of the same area, but have much higher angular resolution, and only weak side lobes. For space use the parts of such a deployable telescope would take advantage of the shape of the shuttle payload bay. On the ground we show that the rectangular array can provide a convenient alt-azimuth telescope when it is fed by a long thin flat mirror whose long axis can be rotated. We consider configurations appropriate for an optical telescone, a sub-mm telescope and a transit telescope. The manufacturing techniques for these fast, and sometimes off-axis, mirrors needs to be proved before these designs can become contenders for the construction of actual telescopes.