For a non-atomic output distribution μ, when all mappings fall within the range of sup-distance τ≤1 from a non-decreasing shape and total variation V≤2, the minimax lower bound on the compound risk is (mn)^{-2/3} + min{τ^2,1/n} + min{τ^2,V^2,(V/n)^{2/3}} (ignoring constant factors).