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 --> H mode threshold scaling P-heat(L-->H) proportional to (n) over bar(e)B(t). Furthermore, contrary to the well known heating power independent Greenwald limit, the L mode density limit increases moderately with rising heating power, (n) over bar(e)(DL) proportional to P-heat(0.3+/-0.1), if a simple power law is assumed. The power dependence becomes more obvious when n analysed in terms of edge densities and powers flowing across the separatrix into the scrape-off layer! n(e)(sep) proportional to P-sep(0.6+/-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.