Bounds are obtained for the solution to the divide-and-conquer recurrence M (n) = F(max;k1+...+kp = n) (M(k1)+M(k2)+...+M(kp)+min(f(k1),...,f(kp))), for nondecreasing functions f. Similar bounds are found for the recurrence with "min" replaced by "sum-of-all-but-the-max." Such recurrences appear in the analysis of various algorithms.