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In an adaptive generalized sidelobe canceler interference signals are canceled when the reference inputs, or auxiliary beams, contain information about those interference signals while not containing information about the mainlobe signal of interest. Assuming a wide sense stationary scenario, the behavior and performance of this adaptive system approach the behavior and performance of the corresponding optimal (Wiener) solution as the adaptive filter stepsize approaches zero. We show here that, with narrowband interferers from the look-direction, time-varying adaptive weight behavior may lead to better performance – in terms of estimating the signal of interest – than that associated with the stationary Wiener solution.