Two optical designs for an F/5 ground-based astronomical telescope, derived by modifying three-mirror designs, are described. The philosophy was to reduce the number of mirrors to two by combining the primary surface and tertiary surface on the same mirror. In the first design, the primary and tertiary mirror surfaces overlap at their vertices and share the same base curvature. Both mirrors are conics of revolution but differ in their conic constants. In the second design the deformation constants are identical. This design is an alternative for a prime focus corrector of a fast (Fp/1.5) primary, yielding sub-arcsecond images over a curved image plane.