Since two decades the richness and potential of natural history collections (NHC) were rediscovered and emphasized, promoting a revolution in the access on data of species occurrence, and fostering the development of several disciplines. Nevertheless, due to their inherent erratic nature, NHC data are plagued by several biases. Understanding these biases is a major issue, particularly because ecological niche models (ENMs) are based on the assumption that data are not biased. Based on it, a recent body of research have focused on searching adequate methods for dealing with biased data and proposed the use of filters in geographical and environmental space. Although the strength of filtering in environmental space has been shown with virtual species, nothing has yet been tested with a real dataset including field validation. In order to contribute to this task, we explore this issue by comparing a dataset from NHC to a recent targeted sampling of the cockroach genus Monastria Saussure, 1864 in the Brazilian Atlantic forest. We showed that, despite strong similarities, the area modeled with NHC data was much smaller. These differences were due to strong climate biases, which increased model's specificity and reduced sensitivity. By applying two forms of rarefaction in the environmental space, we showed that deleting points at random in the most biased climate class is a powerful way for increasing model's sensitivity, so making predictions more suitable to the reality.