  We present a new approximation scheme that allows us to increase the accuracy
of analytical predictions of the power spectra of inflationary perturbations
for two specific classes of inflationary models. Among these models are chaotic
inflation with a monomial potential, power-law inflation and natural inflation
(inflation at a maximum). After reviewing the established first order results
we calculate the amplitudes and spectral indices for these classes of models at
higher orders in the slow-roll parameters for scalar and tensorial
perturbations.
