The suppressive effects of trapping adult sea lampreys, Petromyzon marinus Linnaeus, and releasing sterile males (SMRT) or females (SFRT) into a closed system were expressed in deterministic models. Suppression was modeled as a function of the proportion of the population removed by trapping, the number of sterile animals released, the reproductive rate and sex ratio of the population, and (for the SFRT) the rate of polygyny. Releasing sterile males reduced populations more quickly than did the release of sterile females. For a population in which 30% are trapped, sterile animals are initially released at ratio of 10 sterile to 1 fertile animal, 5 adult progeny are produced per fertile mating, 60% are male, and males mate with an average of 1.65 females, the initial population is reduced 87% by SMRT and 68% by SFRT in one generation. The extent of suppression achieved is most sensitive to changes in the initial sterile release ratio. Given the current status of sea lamprey populations and trapping operations in the Great Lakes, the sterile-male-release technique has the best chance for success on a lake-wide basis if implemented in Lake Michigan. The effectiveness of the sterile-female-release technique should be investigated in a controlled study. Advancing trapping technology should be a high priority in the near term, and artificial rearing of sea lampreys to the adult stage should be a high priority in the long term. The diligent pursuit of sea lamprey suppression over a period of several decades can be expected to yield great benefits.