  This paper discusses the construction of high-performance ground-based
gamma-ray Cherenkov telescopes with a Davies-Cotton reflector. For the design
of such telescopes, usually physics constrains the field-of-view, while the
photo-sensor size is defined by limited options. Including the effect of
light-concentrators in front of the photo sensor, it is demonstrated that these
constraints are enough to mutually constrain all other design parameters. The
dependability of the various design parameters naturally arises once a
relationship between the value of the point-spread functions at the edge of the
field-of-view and the pixel field-of-view is introduced. To be able to include
this constraint into a system of equations, an analytical description for the
point-spread function of a tessellated Davies-Cotton reflector is derived from
Taylor developments and ray-tracing simulations. Including higher order terms
renders the result precise on the percent level.
  Design curves are provided within the typical phase space of Cherenkov
telescopes. The impact of all design parameters on the overall design is
discussed. Allowing an immediate comparison of several options with identical
physics performance allows the determination of the most cost efficient
solution. Emphasize is given on the possible application of solid light
concentrators with their typically about two times better concentration
allowing the use of small photo sensors such as Geiger-mode avalanche photo
diodes. This is discussed in more details in the context of possible design
options for the Cherenkov Telescope Array. In particular, a solution for a
60\,mm(^2) photo sensor with hollow cone is compared to a 36\,mm(^2) with solid
cone.
