  We study constraints that anticipated DEEP survey galaxy counts versus
redshift data will place on cosmological model parameters in models with and
without a constant or time-variable cosmological constant $\Lambda$. This data
will result in fairly tight constraints on these parameters. For example, if
all other parameters of a spatially-flat model with a constant $\Lambda$ are
known, the galaxy counts data should constrain the nonrelativistic matter
density parameter $\Omega_0$ to about 5% (10%, 1.5%) at 1 $\sigma$ with neutral
(worst case, best case) assumptions about data quality.
