  In some cosmological theories with varying constants there are anthropic
reasons why the expansion of the universe must not be too {\it close} to
flatness or the cosmological constant too close to zero. Using exact theories
which incorporate time-variations in $\alpha $ and in $G$ we show how the
presence of negative spatial curvature and a positive cosmological constant
play an essential role in bringing to an end variations in the scalar fields
driving time change in these 'constants' during any dust-dominated era of a
universe's expansion. In spatially flat universes with $\Lambda =0$ the fine
structure constant grows to a value which makes the existence of atoms
impossible.
