We analyze inclusive tau-decay using a modified version of the a expan
sion, a nonperturbative technique in which the effective coupling is a
nalytic in the infrared region. The modification involves renormalizat
ion group improvement of the integrand in a spectral representation fo
r the D-function prior to implementing the a expansion. The advantage
of this approach is that it enables us to monitor the structure of the
induced power corrections and to ensure that these are consistent wit
h the operator product expansion. Numerically the method agrees well w
ith experiment: the comparison is made with the physical quantity R-z
using R-tau as input.