  A new method for predicting inflationary cosmological perturbations, based on
the Wentzel-Kramers-Brillouin (WKB) approximation, is presented. A general
expression for the WKB scalar and tensor power spectra is derived. The main
advantage of the new scheme of approximation is that it is valid even if the
slow-roll conditions are violated. The method is applied to power-law
inflation, which allows a comparison with an exact result. It is demonstrated
that the WKB approximation predicts the spectral indices exactly and the
amplitude with an error lower than 10%, even in regimes far from
scale-invariance. The new method of approximation is also applied to a
situation where the slow-roll conditions hold. It is shown that the result
obtained bears close resemblance with the standard slow-roll calculation.
Finally, some possible improvements are briefly mentioned.
