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A new poll finds that 1 in 10 adults — or 23.5 million Americans — has successfully overcome a problem with alcohol or illegal drugs. The poll also found that 34% of adults had successfully quit smoking.

The telephone survey, which was funded by New York State’s Office of Alcoholism and Substance Abuse Services (OASAS) and conducted in conjunction with the Partnership at Drugfree.org, included responses from more than 2,500 people over 18, who were asked, “Did you used to have a problem with drugs or alcohol but no longer do?”

“This research marks a vitally important step for those who are struggling with addiction by offering clear evidence to support what many know experientially — that millions of Americans have found a path to recovery,” New York State OASAS Commissioner Arlene González-Sánchez said in a statement.

Males and people with lower levels of education were more likely to have kicked a substance problem: 23% of high school dropouts reported having overcome a drug or alcohol issue, compared with just 4% of college graduates. And more men than women reported having quit: 12% versus 7%.

Based on earlier studies, however, these difference don’t suggest that women and college graduates are less likely to succeed in recovery, but rather that they are less likely to have developed problems with addiction in the first place. For example, in addiction treatment, there are typically two men for every woman.

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The survey could not determine some key factors: the severity of the addictions the participants overcame, the obstacles they faced or the methods they used to recover. Contrary to popular perception, most people who quit addictions do so without treatment or participation in self-help groups, and many are able to cut back to non-problematic levels of use, rather than abstaining entirely.

For example, one study of 4,422 people with alcoholism found that one year later, only 25% still met diagnostic criteria for the disorder. Only 25% of participants had received treatment, however, and of those who quit drinking entirely, only half had received help. About one-fifth of the group had quit, while another fifth had successfully moderated their drinking. The rest had some reductions in drinking and were considered only in partial remission or at high risk for relapse. Other studies looking at people with alcoholism and other addictions over longer periods have revealed similar outcomes.

A major 2007 study of the prevalence of addiction in the U.S. population found that while 0.6% had suffered from addiction in the past year, 2.7% had experienced it at some point in their lives, meaning that there were more than three times as many people who once had a problem than who currently did.

But an apparent paradox emerges when people with addictions are studied in different settings. Those who seek treatment or are convicted of drug-related crimes tend to have chronic, relapsing disorders, while surveys of people who have not been incarcerated or treated report short periods of drug misuse that never recur. Most of the difference between these groups is probably due to the fact that the people with the most severe problems are both more likely to get caught and more likely to seek help, while those who can quit on their own simply do so.

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However, research has found that even heroin addicts can and often do recover without assistance. This can be seen in studies of Vietnam veterans: half of vets used opium or heroin at least once and 20% became physically dependent, but only 1% stayed addicted long term, even though most did not receive treatment.

The conflicting results seen in studies of people in treatment versus those in the general population even led the leading journal in the field, Addiction, to devote five articles in its January issue to a debate over whether alcoholism should in fact be classified as a chronic, relapsing disease.

Whatever the case, the National Survey on Drug Use and Health for 2010 found that 8.7% of the American adult population had a substance use disorder within the past year. That’s 22 million people — all of whom could benefit from knowing that recovery is real, possible and common.

Maia Szalavitz is a health writer for TIME.com. Find her on Twitter at @maiasz. You can also continue the discussion on TIME Healthland’s Facebook page and on Twitter at @TIMEHealthland.