  We discuss variants of Cold Dark Matter (CDM) dominated cosmological models
that give good agreement with a range of observations. We consider models with
hot dark matter, tilt, $\Omega < 1$, or a cosmological constant. We also
discuss the sensitivity of the results to other parameters, such as the Hubble
parameter and the baryon fraction. We obtain constraints by combining the COBE
data, cluster abundances, abundance of damped Lyman-$\alpha$ systems at
$z\sim3$, the small-angle Cosmic Microwave Background anisotropy, and the
small-scale non-linear power spectrum. We present non-linear power spectra from
a new suite of N-body simulations for the ``best-bet'' models from each
category.
