  We consider the optimum depth of a cluster survey selected using the
Sunyaev-Zel'dovich effect. By using simple models for the evolution of the
cluster mass function and detailed modeling for a variety of observational
techniques, we show that the optimum survey yield is achieved when the average
size of the clusters selected is close to the size of the telescope beam. For a
total power measurement, we compute the optimum noise threshold per beam as a
function of the beam size and then discuss how our results can be used in more
general situations. As a by-product we gain some insight into what is the most
advantageous instrumental set-up. In the case of beam switching observations
one is not severely limited if one manages to set the noise threshold close to
the point which corresponds to the optimum yield. By defining a particular
reference configuration, we show how our results can be applied to
interferometer observations. Considering a variety of alternative scenarios, we
discuss how robust our conclusions are to modifications in the cluster model
and cosmological parameters. The precise optimum is particularly sensitive to
the amplitude of fluctuations and the profile of the gas in the cluster.
