Summary: The solution of the divide-and-conquer recurrence \[ M(n)=\max_{1\leq k<n}(M(k)+M(n-k)+\min (f(k),f(n-k))) \] is found for a variety of functions f. Asymptotic bounds on M(n) are found for arbitrary nondecreasing f, and the exact form of M(n) is determined for f nondecreasing and weakly concave. As a corollary to the asymptotic bounds, it is shown that M(n) remains linear even when f is almost linear. Among the exact forms determined: For \(f(x)=\lfloor lg x\rfloor\), the solution is \(M(n)=(M(1)+1)n-\lfloor lg n\rfloor -\nu (n)\) where \(\nu\) (n) is the number of 1-bits in the binary representation of n. For \(f(x)=\lceil lg x\rceil\), the solution is \(M(n)=(M(1)+1)n-\lceil lg n\rceil -1\), while for \(f(x)=\lceil lg(x+1)\rceil\), the solution is \(M(n)=(M(1)+2)n-\lfloor lg n\rfloor -\nu (n)-1\).