At temperatures below 238 K, cirrus clouds can form by homogeneous and heterogeneous ice nucleation mechanisms. ECHAM5 contains a two-moment cloud microphysics scheme and permits cirrus formation by homogeneous freezing of solution droplets and heterogeneous freezing on immersed dust nuclei. On changing the mass accommodation coefficient, α, of water vapor on ice crystals from 0.5 in the standard ECHAM5 simulation to 0.006 as suggested by previous laboratory experiments, the number of ice crystals increases by a factor of 14, as a result of the delayed relaxation of supersaturation. At the same time, the ice water path increases by only 29% in the global annual mean, indicating that the ice crystals are much smaller in the case of low α. As a consequence, the short wave and long wave cloud forcing at the top of the atmosphere increase by 15 and 18 W m −2 , respectively. Assuming heterogeneous freezing caused by immersed dust particles instead of homogeneous freezing, the effect is much weaker, decreasing the global annual mean short wave and long wave cloud forcing by 2.7 and 4.7 W m −2 . Overall, these results provide little support, if any, for kinetic growth limitation of ice particles (i.e. a very low α).