This paper presents a frequency domain solution to the delay-type Nehari problem. The solvability condition is formulated in terms of nonsingularities of three matrices. The optimal value y_opt is the maximal value such that one of the three matrices becomes singular when y decreases from +∞ to 0. The all sub-optimal compensators are parameterized in a transparent structure with a modified Smith predictor. The J-spectral factorization of a general para-Hemitian matrix is also given in this paper as a requisite for proof.