  We calculate the corrections to the Sharvin conductance of ballistic
multimode microcontacts that result from electron--electron scattering in the
leads. Using a semiclassical Boltzmann equation, we obtain that these
corrections are {\it positive} and scale with temperature as $T^2\ln(E_F/T)$
for three-dimensional contacts and as $T$ for two-dimensional ones. These
results are relevant to recent experiments on 2DEG contacts.
