The two-mirror telescopes/cameras that have no coma, no spherical aberration and arbitrarily fast focal ratios form a two-parameter (s, K) family of exact optical designs analytically derived earlier. We explore the full range of these designs in the s-K plane. Here s is the mirror separation/focal length and K is the distance from secondary to focus/focal length. Besides perfect-focus analogues of most well-known telescope designs, there are families of spectrograph cameras, X-ray telescopes and solar furnaces. Systems with s= 2 have minimum astigmatism and have exceptionally good images.