Atmospherically important data are gained from cloud condensation nucleus counter (CCNC) analysis of aerosols that are particle mobility separated using differential mobility analysers (I)MA). We present relaxed step functions that can be fitted to these data to obtain critical diameters or critical supersaturations. The step functions are based on the DMA transfer function. We treat the case with fixed supersaturation and varied particle diameter as well as fixed particle size and varied supersaturation. Comparison with experimental data shows that the width of the DMA transfer function controls the steepness of the relaxed step function. The less steep slope in the activation curve caused by the presence of a slightly soluble compound in the particle is discussed. Also in this case, the DMA transfer function width influences the steepness of the activation curve. Finally we demonstrate the errors made if doubly charged particles are not accounted for and a wide DMA transfer function is used. (C) 2008 Elsevier Ltd. All rights reserved.