Background: We have developed an approach for modelling the health impact of introducing new smoke-free tobacco products. We wished to compare its estimates with those of alternative approaches, when applied to snus, used in Sweden for many years., Methods: Modelling was restricted to men aged 30-79 years for 1980-2009 and to four smoking-related diseases. Mortality data were extracted for Sweden and other European countries. Published data provided Swedish prevalence estimates for combinations of never/former/current smoking and snus use, and smoking prevalence estimates for other European countries. Approach 1 compares mortality in Sweden and in other countries with a smoking prevalence similar to Sweden's prevalence of combined smoking/snus use. Approaches 2 and 3 compare mortality in Sweden with hypothetical mortality had snus users smoked. Approach 3 uses our health impact model, individuals starting with the tobacco prevalence of Sweden in 1980. Tobacco histories during 30-year follow-up were then estimated using transition probabilities, with risk derived using a negative exponential model. Approach 2 uses annual tobacco prevalence estimates coupled with estimates of relative risk of current and former smokers regardless of history. The main applications of Approaches 2 and 3 assume that only smoking affects mortality, though sensitivity analyses using Approach 3 allow for risk to vary in snus users and dual users., Results: Using Approach 2, estimated mortality increases in Sweden in 1980-2009 had snus not been introduced were: lung cancer 8786; COPD 1781; IHD 10,409; stroke 1720. The main Approach 3 estimates were similar (7931, 1969; 12,501; 1901). They decreased as risk in snus users and dual users increased. Approach 1 estimates differed wildly (77,762, 32,538; 77,438; 76,946), remaining very different following correction for differences between Sweden and the comparison countries in non-smoking-related disease mortality., Conclusions: Approach 1 is unreliable, accounting inadequately for non-tobacco factors affecting mortality. Approaches 2 and 3 provide reasonably similar approximate estimates of the mortality increase had snus not been available, but have differing advantages and disadvantages. Only Approach 3 considers tobacco history, but develops histories using tobacco transition probabilities, which is possibly less reliable than using estimated tobacco prevalences at each follow-up year.