  We propose a simple and easy-to-implement scheme for a renormalon-free gluon
condensate (GC) matrix element, which is analogous to implementations of
short-distance heavy-quark mass renormalization schemes existing in the
literature already for a long time. Because the scheme is based on a
perturbative subtraction at the level of the matrix element, with a freely
adaptable infrared factorization scale, it can be implemented with little
effort for any observable where the GC is relevant. The scheme depends on the
renormalon norm of the GC which has to be supplemented independently. We apply
the scheme to the fixed-order (FOPT) and contour-improved (CIPT) perturbative
expansions of $\tau$ hadronic spectral function moments. These expansions
exhibit a long-standing discrepancy for moments used in high-precision
determinations of the strong coupling in the commonly used GC scheme that is
not renormalon-free. We show that the scheme is capable of resolving the
FOPT-CIPT discrepancy problem. At the same time, the perturbative behaviour of
the moments that previously showed bad convergence properties and for which the
non-perturbative corrections from the GC are sizeable, is substantially
improved. The new GC scheme may provide a powerful theoretical tool for future
phenomenological applications.
