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An iterative estimation procedure involving the use of a light limiter is proposed for obtaining robust estimates of the amplitude of a signal of known form in additive nearly Gaussian noise. In the case of a constant signal the procedure, referred to as the iterative limiter estimator (ILE), is exhibited as a form of stochastic approximation and the procedure is shown to be robust in a well-defined asymptotically min-max sense. The ILE is also shown to be asymptotically robust in terms of efficiency relative to the sample mean. in the case of a time-varying signal the procedure is referred to as an iterative limiter-correlator estimator (ILCE). Simulation results show that both the ILE and the ILCE possess a high degree of robustness for seemingly mild, but potent, deviations from the Gaussian model. This robustness is obtained at the expense of a relatively small loss in efficiency when the noise is actually Gaussian.