The paper investigates bolometrically determined radiation power profiles, energy exhaust and impurity accumulation in the two types of H-mode in ASDEX. During the burst dominated H-mode, the repetitive burst-like energy and particle expulsion into the divertor prevents an increase of radiation within the outer half of the plasma minor radius. This type of H-mode arrives at an equilibrium state. During the burst free H-mode, the radiation power losses, unimpeded by bursts, grow over the entire plasma cross-section until this H-mode ends in radiation collapse. Impurity accumulation, resulting in central peaking of the radiation power profiles, takes place in both types of H-mode. The time evolutions of the central radiation power density and the predominantly responsible iron concentration are not significantly affected by the presence or absence of bursts. However, to establish the burst free H-mode, it is required that the absolute values of the iron concentration and the associated radiation power losses at the plasma centre exceed given threshold values. This critical level can be achieved either by external injection of medium-Z metals or by sufficiently strong accumulation of intrinsic metallic impurities during a preceding burst dominated H-phase.