In some parts of the USA and in Canada smouldering cigarettes are required to extinguish if placed on a certain number of layers of filter paper. This is usually achieved by the use of bands on the cigarette paper, which reduce oxygen diffusion into the cigarette. From a smoker's perspective, however, it is desirable that a cigarette does not extinguish if left to smoulder, for example, in an ash tray. To facilitate the design of papers for such cigarettes the influence of various cigarette parameters on self-extinguishment is investigated by numerical simulation of a one-dimensional cigarette model, which describes the main thermodynamic behaviour of smouldering cigarettes. The tobacco density, the tobacco heat capacity, the width of the bands on the cigarette paper and the heat released during combustion are chosen as parameters whose influence on the required oxygen diffusion constant of the bands on the cigarette paper is investigated. As these parameters are subject to a certain variation, it is assumed that the parameters are independently normally distributed. Based on this assumption the probability that a cigarette with given mean parameter values will extinguish, is calculated numerically. The results show that the admissible range of diffusion constants for the bands on the cigarette paper is in general quite small and it is reduced even further if statistical variations of the cigarette parameters are considered. The results provide guidelines for the appropriate choice of the diffusion constant of the bands on the cigarette paper such that the cigarettes comply with legal requirements and do not extinguish during normal smoking.