If $P\subset{\bf R}^{n}$ is a Delzant polytope and $A$ is a smooth function on $\overline{P}$ with the property that $L_{A}(f)$ vanishes if $f$ is affine linear and $L_{A}(f)>0$ if $f$ is a convex function which is not affine linear, then there is an admissible symplectic potential satisfying the equation $u_{ij}^{ij}=-A$.