Fuzzy Cognitive Maps are widely applied to support decision making tasks. It is often hard for experts to create the model of a system that provides the required accuracy but simple enough to easily use in practice. In general, it is better to create complex models first, because they can be computationally reduced later until they preserve the required accuracy but become simple enough. Two novel Fuzzy Cognitive Map reduction methods based on K-Means and Fuzzy C-Means clustering are suggested in order to generate simplified models that hopefully mimic the behavior of the original model better than the already existing methods. After the quick overview of the existing techniques found in literature, a simple and a complex model of a real-life problem are reduced to varying degrees with the suggested new methods and with an existing one. The first results of the comparison are published in this paper, too.