The origin and evolution of species ranges remains a central focus of historical biogeography and the advent of likelihood methods based on phylogenies has revolutionized the way in which range evolution has been studied. A decade ago, the first elements of what turned out to be a popular inference approach of ancestral ranges based on the processes of Dispersal, local Extinction and Cladogenesis (DEC) was proposed. The success of the DEC model lies in its use of a flexible statistical framework known as a Continuous Time Markov Chain and since, several conceptual and computational improvements have been proposed using this as a baseline approach. In the spirit of the original version of DEC, we introduce DEC eXtended (DECX) by accounting for rapid expansion and local extinction as possible anagenetic events on the phylogeny but without increasing model complexity (i.e. in the number of free parameters). Classical vicariance as a cladogenetic event is also incorporated by making use of temporally flexible constraints on the connectivity between any two given areas in accordance with the movement of landmasses and dispersal opportunity over time. DECX is built upon a previous implementation in C/C++ and can analyze phylogenies on the order of several thousand tips in a few minutes. We test our model extensively on Pseudo Observed Datasets and on well-curated and recently published data from various island clades and a worldwide phylogeny of Amphibians (3309 species). We also propose the very first implementation of the DEC model that can specifically account for trees with fossil tips (i.e. non-ultrametric) using the phylogeny of palpimanoid spiders as a case study. In this paper, we argue in favour of the proposed improvements, which have the advantage of being computationally efficient while toeing the line of increased biological realism.