In this paper, generalized Nevanlinna-Pick theory is used to solve a time-domain constrained H-infinity control problem for linear time-invariant discrete-time systems. First it is shown that if constraints are imposed only over a finite horizon (i.e., only on the first n samples), then the problem reduces to a finite-dimensional convex minimization problem. Subsequently it is shown that if these problems are conveniently modified, then letting the horizon length go to infinity produces a solution to the infinite-horizon problem.