The study objectives were to determine the effects of smoking machine puffing parameters on mainstream smoke composition and to express those effects as predicting relationships. Forty-eight commercial Philip Morris USA and Philip Morris International cigarettes from international markets and the 1R4F reference cigarette were machine-smoked using smoking conditions defined by the International Organization of Standardization (ISO), the Massachusetts Department of Public Health (MDPH), and Health Canada (HC). Cigarette tobacco fillers were analyzed for nitrate, nicotine, tobacco-specific nitrosamines (TSNA), and ammonia. Mainstream yields for tar and 44 individual smoke constituents and "smoke pH" were determined. Cigarette constituent yields typically increased in the order ISO<MDPH<HC. Relative yield increases were generally greater for cigarettes with higher initial filter ventilation and were also generally greater for vapor-phase constituents than for particulate-phase constituents. Predicting relationships were developed between ISO tar and ISO, MDPH, and HC constituent yields and between MDPH tar and HC tar and respective smoking condition yields. MDPH and HC constituent yields could be predicted with similar reliability using ISO tar or the corresponding smoking-condition tar. The reliability of the relationships varied from strong to weak, depending on particular constituents. Weak predicting relationships for nitrogen oxides and TSNA's, for example, were improved with inclusion of tobacco filler composition factors. "Smoke pH" was similar for all cigarettes at any one smoking condition, and overall marginally lower at HC conditions than at ISO or MDPH conditions.