The prevalence of strong brands such as Coca-Cola, McDonald’s, Budweiser, and Marlboro in “vice” categories has important implications for regulators and consumers. While researchers in multiple disciplines have studied the effectiveness of anti-tobacco counter-marketing strategies, little attention has been given to how brand strength may moderate the efficacy of tactics such as excise taxes, usage restrictions, and educational advertising campaigns. In this research, we use a multiple discrete-continuous model to study the impact of anti-smoking techniques on smokers’ choices of brands and quantities. Our results suggest that while cigarette excise taxes decrease smoking rates, these taxes also result in a shift in market share towards stronger brands. Market leaders may be less affected by tax policies because their market power allows strong brands such as Marlboro to absorb rather than pass through increased taxes. In contrast, smoke-free restrictions cause a shift away from stronger brands. In terms of anti-smoking advertising we find minimal effects on brand choice and consumption. The findings highlight the importance of considering brand asymmetries when designing a policy portfolio cigarette tax hikes, smoke-free restrictions, and anti-smoking advertising campaigns.