In this talk, I will present a new bound for solutions to the Poisson problem associated with the weighted one-Laplacian. The Aleksandrov–Bakelman–Pucci (ABP) estimate has long been a fundamental tool in the regularity theory of fully nonlinear elliptic equations. More recently, it has been extended to certain degenerate and singular equations, including the p-Laplacian. In contrast, we consider an ABP-type estimate for the weighted one-Laplacian, which exhibits much stronger degeneracy, since it controls second-order derivatives only in directions orthogonal to the gradient of the solution. Our analysis is based on the properties of the contact set of the solution and its quasiconcave envelope.