According to researchers writing in The Lancet, we’re doing a good job of reducing the number of premature deaths—those occurring in people under 70. And if current trends continue with some improvements, such early deaths should drop by 40% over the next two decades.

When a group of 16 researchers from across the world looked at mortality trends from 2000 to 2010, they were encouraged by the results. “We actually found that mortality is falling very rapidly,” says lead author Ole Norheim, professor of global public health at the University of Bergen, Norway–by one-third for children and one-sixth for everyone below age 70. In low-income countries, where avoiding premature death is often more challenging due to weaker health systems and infectious diseases, the news was even better — deaths fell by an even larger percentage: 24% over the last ten years.

A number of factors are responsible, Norheim says, including improvements in child and maternal health, more effective ways to combat infectious diseases, economic factors, and cleaner water. “I don’t think people realize how positive these trends are and how important this would be for health worldwide,” he says. “People’s probability of surviving up to the age of 70 is actually much, much better now, compared to 1970.”

If those trends continue, and get even better, the 40% reduction over the next 20 years is both realistic and possible, Norheim says. One thing that would accelerate the process — helping more people to quit smoking. While preventive services, access to vaccines, treatments, and better nutrition are critical for hitting the goal, “If prices [of cigarettes] were doubled, that would reduce smoking by 1/3. That would mean millions of lives saved,” he says.

Write to Mandy Oaklander at mandy.oaklander@time.com.