  It is well known that point-contact Andreev reflection spectroscopy provides
reliable measurements of the energy gap(s) in a superconductor when the contact
is in the ballistic or nearly-ballistic regime. However, especially when the
mean free path of the material under study is small, obtaining ballistic
contacts can be a major challenge. One of the signatures of a Maxwell
contribution to the contact resistance is the presence of "dips" in the
differential conductance, associated to the sudden appearance of a Maxwell
term, in turn due to the attainment of the critical current of the material in
the contact region. Here we show that, using a proper model for the $R(I)$ of
the material under study, it is possible to fit the experimental curves
(without the need of normalization) obtaining the correct values of the gap
amplitudes even in the presence of such dips, as well as the temperature
dependence of the critical current in the contact. We present a test of the
procedure in the case of Andreev-reflection spectra in
Mg$_{0.85}$Al$_{0.15}$B$_2$ single crystals.
