Both cigarette smoke and inhaled asbestos fibres can cause lung cancer, but the assessment of how these agents act in combination is a matter of great difficulty. In non-smokers, the condition is so rare that, in any cohort of asbestos workers, the standardised mortality ratio (SMR, that is the ratio of the numbers of deaths observed and expected) is quite imprecise. The SMR for smokers, with which it has to be compared, is also subject to sampling error, making the interaction even more unstable. This accounts for much of the variation that has bedevilled evaluation. The debate has been concentrated on two hypotheses: additive (asbestos and cigarette smoke act independently) and multiplicative (asbestos produces an effect proportional to the effect of smoking). The very few data available until 1977 failed to fit the former and fitted the latter only poorly. They would have fitted better a hypothesis of greater synergism, but the only one proposed was too convoluted. So the multiplicative model appeared the only alternative, and was deemed 'accepted'. The ratio of lung cancer SMRs for non-smokers and smokers was generalised into the relative asbestos effect, RAE, with all the advantages of a parametric statistic (Berry et al., 1985, British Journal of Industrial Medicine 42, 12). On the multiplicative hypothesis, RAE=1, while RAE>1 indicates less synergism. The RAEs for the three most recent of the six results then available were >1; for one, P<0.005. From the six results combined, it was concluded that 'overall non-smokers have a relative risk of lung cancer due to asbestos that is 1.8 times that of smokers'. Some admitted uncertainty about the figure 1.8 was seized upon and even the thrust of the conclusion has been very largely disregarded. So too has the RAE and all its benefits. As a result, all later reviewers have been led into error, much of it serious: in particular, they have failed to appreciate how much of the variation arises from the inevitable imprecision of all RAEs. This failure led reviewers in 1994 to discard, quite without justification, those interactions which were less than multiplicative and came from cohort studies. Although case-referent studies seemed to support the multiplicative hypothesis, the information from them is essentially unreliable. Thus it cannot weaken the conclusions from the cohort studies, that the multiplicative hypothesis is untenable and that the relative risk of lung cancer from asbestos exposure is about twice as high in non-smokers as in smokers; the best estimate of RAE is 2.04, with 95% confidence interval 1.28-3.25. This finding is not only of high statistical significance but of great social and scientific importance.