A ripple-free deadbeat controller for a system exists if and only if there are no transmission zeros coinciding with the poles of the reference signal. Approaches to this problem often use the Diophantine equation solution. However, solutions provided by the Diophantine equation often exhibit extremely bad transient responses. This approach gives a new affine parametrization of solutions of the Diophantine equation. Based on this parametrization, LMI conditions are used to provide optimal or constrained controllers for design quantities such as overshoot, undershoot, control amplitude,'slew rate' as well as for norm bounds such as l(1), l(2) and l(infinity).