The L mode and H mode density operational window in the vicinity of the density limit has been investigated with a combination of gas puff refuelling and improved fine tuning of neutral beam injection (NBI) heating power. In this way, a novel strategy is achieved by means of a parallel increase of density and heating power. As the density limit is approached, H modes degrade into L modes independently of heating power; this is in contrast to the generally accepted L to H mode threshold scaling PheatL-H varies as neB. Furthermore, contrary to the well known heating power independent Greenwald limit, the L mode density limit increases moderately with rising heating power, neDL varies as Pheat0.3+or-0.1, if a simple power law is assumed. The power dependence becomes more obvious when analysed in terms of edge densities and powers flowing across the separatrix into the scrape-off layer, nesep varies as Psep0.6+or-0.2. The corresponding H mode studies show that before an H mode quenches into an L mode the maximum achievable density (i.e. The H mode density limit) is practically independent of the heating power, as observed on many machines