The depth-of-field of imaging systems can be enhanced by placing a phase mask in their aperture stop and deconvolving the image. In general, the mask is optimized using a closed-form image quality criterion assuming deconvolution with a Wiener filter. However, nonlinear deconvolution algorithms may have better performance, and the question remains as to whether a better co-designed system could be obtained from optimization with a criterion based on such algorithms. To investigate this issue, we compare optimization of phase masks with criteria based on the Wiener filter and on a nonlinear algorithm regularized by total variation. We show that the obtained optimal masks are identical, and propose a conjecture to explain this fact. This result is important since it supports the frequent co-design practice consisting of optimizing a system with a closed-form criterion based on linear deconvolution and deconvolving with a nonlinear algorithm.