Introduction To test whether urges to smoke and perceived addiction to smoking have independent predictive value for quit attempts and short-term quit success over and above the Heaviness of Smoking Index (HSI). Aims and Methods Data were from the International Tobacco Control Four Country Smoking and Vaping Wave 1 (2016) and Wave 2 (2018) surveys. About 3661 daily smokers (daily vapers excluded) provided data in both waves. A series of multivariable logistic regression models assessed the association of each dependence measure on odds of making a quit attempt and at least 1-month smoking abstinence. Results Of the 3661 participants, 1594 (43.5%) reported a quit attempt. Of those who reported a quit attempt, 546 (34.9%) reported short-term quit success. Fully adjusted models showed that making quit attempts was associated with lower HSI (adjusted odds ratio [aOR] = 0.81, 95% confidence interval [CI] = 0.73 to 0.90, p < .001), stronger urges to smoke (aOR = 1.08, 95% CI = 1.04 to 1.20, p = .002), and higher perceived addiction to smoking (aOR = 0.52, 95% CI = 0.32 to 0.84, p = .008). Lower HSI (aOR = 0.57, 95% CI = 0.40 to 0.87, p < .001), weaker urges to smoke (aOR = 0.85, 95% CI = 0.76 to 0.95, p = .006), and lower perceived addiction to smoking (aOR = 0.55, 95% CI = 0.32 to 0.91, p = .021) were associated with greater odds of short-term quit success. In both cases, overall R2 was around 0.5. Conclusions The two additional dependence measures were complementary to HSI adding explanatory power to smoking cessation models, but variance explained remains small. Implications Strength of urges to smoke and perceived addiction to smoking may significantly improve prediction of cessation attempts and short-term quit success over and above routinely assessed demographic variables and the HSI. Stratification of analyses by age group is recommended because the relationship between dependence measures and outcomes differs significantly for younger (aged 18–39) compared to older (aged older than 40) participants. Even with the addition of these extra measures of dependence, the overall variance explained in predicting smoking cessation outcomes remains very low. These measures can only be thought of as assessing some aspects of dependence. Current understanding of the factors that ultimately determine quit success remains limited.