  We propose a non-perturbative method for defining the higher dimensional
operators which appear in the Heavy Quark Effective Theory (HQET), such that
their matrix elements are free of renormalon singularities, and diverge at most
logarithmically with the ultra-violet cut-off. Matrix elements of these
operators can be computed numerically in lattice simulations of the HQET. We
illustrate our procedures by presenting physical definitions of the binding
energy ($\lb$) and of the kinetic energy (-$\lambda_1/2m_Q$) of the heavy quark
in a hadron. This allows us to define a ``subtracted pole mass", whose inverse
can be used as the expansion parameter in applications of the HQET.
