We introduce a new method, called the {\it parametric minimum
cross-entropy} (PME) method, for rare event probability estimation and
counting with a particular emphasis on the satisfiability problem.
The PME method is derived from the well known Kullback's minimum
cross-entropy method, called {\it MinxEnt}. It is based on the
marginal distributions derived from the optimal joint MinxEnt
distribution and is a parametric version of it. Similar to the {\it
cross-entropy} (CE) method, the PME algorithm first casts the
underlying counting problem into an associated rare-event probability
estimation problem, and then finds the optimal parameters of the
importance sampling distribution to estimate efficiently the desired
quantity. We present supportive numerical results for counting the
number of satisfiability assignments and compare PME with the CE
method. Our numerical results suggest that the PME method is superior
to CE. This is based on the fact that for the satisfiability problem
and some other ones involving separable functions the optimal
parameters of the importance sampling distribution can be estimated
better with the MinxEnt type procedure, rather than with indicators.