This paper studies small area estimation of computationally complex poverty indicators; more concretely, we study fuzzy monetary and fuzzy supplementary poverty indicators. These two indicators do not need to set a poverty line because they are based on the degree of poverty of each individual relative to the population to which it belongs. Moreover, the latter takes into account the non- monetary and multidimensional nature of poverty. For this, a faster version of the empirical best/bayes (EB) method of Molina and Rao (2010) is proposed. This new method allows feasible estimation of computationally complex indicators in large populations, and can still reduce considerably the computation time when the original EB method is feasible. In simulations, the proposed fast EB method is compared with the original EB method when estimating the mentioned indicators along with the poverty incidence in small areas. Results show negligible loss of efficiency of the fast EB method as compared to the original one, while allowing estimation of complex indicators that require sorting all population elements. The method is applied to the estimation of poverty indicators in the region of Tuscany, both at province and municipality levels, using data from the Italian Survey on Income and Living Conditions.