In this note is shown how discrete-time, mixed-sensitivity, l(1)-optimal control problems can be converted via polynomial techniques to linear "least absolute data fitting" problems and Solved via efficient and stable numerical methods, In particular, two new sub/superoptimization schemes are introduced by expressing the closed-loop sensitivity and complementary sensitivity maps in terms of the free parameter of a stabilizing deadbeat controller parameterization and exploiting the underlying algebraic structure. This approach induces the application of a consistent truncation strategy that leads to a redundance-free constraint formulation and, as a consequence, to linear programming problems less affected by degeneracy, Further, more insight on the algebraic structure of the problem and on the achievement of exact rational solutions is provided, allowing the development of a simple and conceptually attractive theory.