  We analyze inclusive $\tau$ decay using a modified version of the $a$
expansion, a non-perturbative technique in which the effective coupling is
analytic in the infrared region. The modification involves renormalization
group improvement of the integrand in a spectral representation for 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 with the operator product
expansion. Numerically the method agrees well with experiment: the comparison
is made with the physical quantity $R_Z$ using $R_\tau$ as input.
