We discuss the infinite horizon H(infinity)-control problem by state-feedback for a linear time invariant plant which is not restricted with respect to its finite or infinite zero structure. We provide an algebraic characterization for the optimal value to be attained in terms of the solvability of a nonstrict Riccati inequality and propose possibilities for verifying these criteria. If the optimum is not achieved we give a complete test for the need of high-gain feedback in order to approach the optimal value.