Recent studies have shown that starburst dwarf galaxies have steeply rising rotation curves in their inner parts, pointing to a close link between the intense star formation and a centrally concentrated mass distribution (baryons and dark matter). More quiescent dwarf irregulars typically have slowly rising rotation curves, although some `compact' irregulars with steep, inner rotation curves exist. We analyse archival Hubble Space Telescope images of two nearby `compact' irregular galaxies (NGC 4190 and NGC 5204), which were selected solely on the basis of their dynamical properties and their proximity. We derive their recent star formation histories by fitting colour-magnitude diagrams of resolved stellar populations, and find that the star formation properties of both galaxies are consistent with those of known starburst dwarfs. Despite the small sample, this strongly reinforces the notion that the starburst activity is closely related to the inner shape of the potential well.