Some harm reduction strategies encourage individuals to switch from a harmful addictive good to a less harmful addictive good; examples include e-cigarettes (substitutes for combustible cigarettes) and methadone and buprenorphine (substitutes for opioids). Harm reduction methods have proven to be controversial. Advocates argue that addicts benefit because they can switch to a less harmful substance, but opponents argue that this could increase addiction and even encourage non-users to begin using the addictive goods. This paper builds on theories of addiction to model the introduction of a harm reduction method, and it demonstrates the conditions under which each side is correct; i.e. the conditions under which introducing a harm reduction method can lead to quitting of the original addictive good, and the conditions under which it can lead previous abstainers to begin using the harm reduction method and even the original, more harmful, addictive good. Knowledge of these conditions is helpful for understanding the consequences of harm reduction methods in various markets.