  We revisit the issue of cosmological parameter estimation in light of current
and upcoming high-precision measurements of the cosmic microwave background
power spectrum. Physical quantities which determine the power spectrum are
reviewed, and their connection to familiar cosmological parameters is
explicated. We present a set of physical parameters, analytic functions of the
usual cosmological parameters, upon which the microwave background power
spectrum depends linearly (or with some other simple dependence) over a wide
range of parameter values. With such a set of parameters, microwave background
power spectra can be estimated with high accuracy and negligible computational
effort, vastly increasing the efficiency of cosmological parameter error
determination. The techniques presented here allow calculation of microwave
background power spectra $10^5$ times faster than comparably accurate direct
codes (after precomputing a handful of power spectra). We discuss various
issues of parameter estimation, including parameter degeneracies, numerical
precision, mapping between physical and cosmological parameters, and systematic
errors, and illustrate these considerations with an idealized model of the MAP
experiment.
