  We study the mode-coupling approximation for the KPZ equation in the strong
coupling regime. By constructing an ansatz consistent with the asymptotic forms
of the correlation and response functions we determine the upper critical
dimension d_c=4, and the expansion z=2-(d-4)/4+O((4-d)^2) around d_c. We find
the exact z=3/2 value in d=1, and estimate the values 1.62, 1.78 for z, in
d=2,3. The result d_c=4 and the expansion around d_c are very robust and can be
derived just from a mild assumption on the relative scale on which the response
and correlation functions vary as z approaches 2.
