  We present a formulation to give renormalon-free predictions consistently
with fixed order perturbative results. The formulation has a similarity to
Lee's method in that the renormalon-free part consists of two parts: one is
given by a series expansion which does not contain renormalons and the other is
the real part of the Borel integral of a singular Borel transform. The main
novel aspect is to evaluate the latter object using a dispersion relation
technique, which was possible only in the large-$\beta_0$ approximation. Here,
we introduce an "ambiguity function," which is defined by inverse Mellin
transform of the singular Borel transform. With the ambiguity function, we can
rewrite the Borel integral in an alternative formula, which allows us to obtain
the real part using analytic techniques similarly to the case of the
large-$\beta_0$ approximation. We also present detailed studies of
renormalization group properties of the formulation. As an example, we apply
our formulation to the fixed-order result of the static QCD potential, whose
closest renormalon is already visible.
