X-ray-selected BL Lacs (XBLs) are generally thought to outnumber the more extreme radio-selected objects (RBLs), on the grounds that their properties could be understood if the X-ray jet were broader than the radio one. Here we present an alternative explanation: RBLs and XBLs may well be two aspects of the same population, whose main difference is the frequency of the high-energy cut-off in their energy distribution, with XBLs constituting the small subclass with cut-offs at X-ray (or higher) energies. Under this assumption, we are able to reproduce the X-ray number counts of XBLs starting from the radio counts of RBLs. We also calculate the distribution of radio fluxes of BL Lacs in current and future (deeper) X-ray surveys (e.g ROSAT), wherein we predict that a strong selection effect arising from radio constraints will lead to the preferential discovery of objects of the RBL kind. our hypothesis implies that there is a single family of BL Lacs and that, within this family, XBL-like objects are a small minority, contrary to the common belief that they represent the most numerous class.