We apply Christ's method of refinements to the l_p-improving problem
for discrete averages A_N along polynomial curves in Z^d. Combined with certain elementary estimates for the number of solutions to certain special
systems of diophantine equations, we obtain some restricted weak-type p \to p'
estimates for the averages A_N in the subcritical regime. The dependence on
N of the constants here obtained is sharp, except maybe for an epsilon-loss.