Hankel norm and Nehari-type approximation problems arise in model reduction and H-x-control theory. Existing solutions to the discrete-time version of these problems ma he derived using a standard state-space framework, but the resulting solution formulas require an invertible. A-matrix. As a further complication, the D-matrix in the representation formula for all solutions becomes unbounded in the optimal case. The aim of this paper is to show that both these complications may be removed by analyzing these problems in a descriptor framework.