Small area estimation techniques typically rely on mixed models containing random area effects to characterise between area variability. In contrast, Chambers and Tzavidis (2006) describe an approach to small area estimation based on regression M!quantiles. This approach avoids conventional Gaussian assumptions and problems associated with specification of random effects, allowing between area differences to be characterized by the variation of area!specific M!quantile coefficients. However, the resulting M!quantile predictors of small area means can be biased. In this paper we propose a general framework for robust bias adjusted small area prediction that corrects this problem, and is based on representing a small area predictor as a functional either of the Chambers and Dunstan (1986) or of the Rao!Kovar!Mantel (1990) predictor of the within area distribution of the target variable.