  Analyses of peculiar velocity surveys face several challenges, including low
signal--to--noise in individual velocity measurements and the presence of
small--scale, nonlinear flows. This is the second in a series of papers in
which we describe a new method of overcoming these problems by using data
compression as a filter with which to separate large--scale, linear flows from
small--scale noise that can bias results. We demonstrate the effectiveness of
our method using realistic catalogs of galaxy velocities drawn from N--body
simulations. Our tests show that a likelihood analysis of simulated catalogs
that uses all of the information contained in the peculiar velocities results
in a bias in the estimation of the power spectrum shape parameter $\Gamma$ and
amplitude $\beta$, and that our method of analysis effectively removes this
bias. We expect that this new method will cause peculiar velocity surveys to
re--emerge as a useful tool to determine cosmological parameters.
