We consider three alternative parametric models to describe genetic and environmental influences on smoking initiation and smoking persistence. Under the single liability dimension model, the same genetic and environmental influences which determine smoking initiation also influence smoking persistence. Under the independent liability dimensions model, independent initiation and persistence dimensions determine onset of smoking, and persistence in those who become smokers. The combined model also postulates separate initiation and persistence dimensions, but allows for the possibility that some smokers are so low on liability to smoke on the initiation dimension that they become ex-smokers for this reason. Reanalysis of London twin data published by Eaves and Eysenck support the single liability dimension model. We discuss the difficulty of reconciling this finding with the hypothesis that nicotine dependence is a major determinant of smoking persistence, but caution that sample sizes in the London twin study were small.