We show the advantages of a wedding cake design for Sunyaev-Zel'dovich
cluster surveys. We show that by dividing up a cluster survey into a wide and a
deep survey, one can essentially recover the cosmological information that
would be diluted in a single survey of the same duration due to the
uncertainties in our understanding of cluster physics. The parameter degeneracy
directions of the deep and wide surveys are slightly different, and combining
them breaks these degeneracies effectively. A variable depth survey with a few
thousand clusters is as effective at constraining cosmological parameters as a
single depth survey with a much larger cluster sample.Comment: 4 figures, 1 table; revised versio