A computationally tractable design method is presented, which explicitly yields the entire set of all constant-gain controllers which robustly stabilize a family of systems with uncertainty. A desired "optimal" controller may then be selected from the feasible set. The method applies to the class of systems where a delay element e(-hs) with interval (finite or infinite) uncertainty about h, is followed by a plant characterized by a rational transfer function with independent interval coefficients. Illustrative numerical examples are provided.