IRLS, but without having a line to fit.

My boss told me to think about applying the iteratively reweighted least squares to fitting a static data set.  So it's not really least squares so much as iteratively reweighted weighted means.  And in the single dimension test case I knocked together in about ten minutes, it converges in about five iterations to the correct solution for basically all contamination rates up to the point where the contaminated sample is 100% the size of the real sample.  This makes it switch over to fitting the contaminating sample.  Makes sense.