  We exploit a new numerical technique for evaluating the tree order
contributions to the primordial scalar and tensor power spectra for scalar
potential models of inflation. Among other things we use the formalism to
develop a good analytic approximation which goes beyond generalized slow roll
expansions in that (1) it is not contaminated by the physically irrelevant
phase, (2) its 0th order term is exact for constant first slow roll parameter,
and (3) the correction is multiplicative rather than additive. These features
allow our formalism to capture at first order, effects which are higher order
in other expansions. Although this accuracy is not necessary to compare current
data with any specific model, our method has a number of applications owing to
the simpler representation it provides for the connection between the power
spectra and the expansion history of a general model.
