Two specific extensions for fluctuation analysis are considered here: mutants are sampled from only a fraction of the final cultures, also called plating efficiency, and the final number of cells is no longer assumed to be constant from one culture to another. We are focusing in this paper to the extension of three specific robust methods: the classic P0 method of Luria and Delbrück, the Maximum Likelihood and a method based on the generating function of the mutant count. Unbiased estimators are thus proposed. Their asymptotic variances are computed. These statistical properties are illustrated with simulation experiments. The methods are also applied to real data sets. In particular, the results are compared with those obtained using previous methods.