The level of fertility in the majority of European countries is deeply below the replacement level. On the other hand, in the case of some ethnic groups, fertility continues to be on an above‐average level. One such example is the Romany population of Slovakia, especially those in very poor, segregated settlements. Very likely, there are strong interconnections between regional disparities, social and cultural segregation and reproduction of Romany. The study tries to discover them. We perform factor and cluster analyses in order to identify major factors which differentiate and create clusters in the set of 79 Slovak local administrative unit (LAU‐1) districts from the view point of above‐replacement fertility levels. Using the transversal and cohort approaches, another aim is to identify major specificities of Romany reproduction and the range of lag behind the majority population in terms of demographic transition. The concept of ‘high fertility trap’ is presented in this respect.