  Measurements of the flux and redshifts of Type Ia supernovae have provided
persuasive evidence that the expansion of the universe is accelerating. If
true, then in the context of standard FRW cosmology this suggests that the
energy density of hte universe is dominated by "dark energy" -- a component
with negative pressure of magnitude comparable to its energy density. To
further investigate this phenomenon, more extensive surveys of supernovae are
being planned. Given the likely timescales for completion, by the time data
from these surveys are available some important cosmological parameters will be
known to high precision from CMB measurements. Here we consider the impact of
that foreknowledge on the design of supernova surveys. In particular we show
that, despite greater opportunities to multiplex, purely from the point of view
of statistical errors, a deep survey may not obviously be better than a shallow
one.
