They knew it was a cool painting. But Buck Burns and David Van Auker hadn’t thought it a masterpiece until visitors to their New Mexico furniture and antiques shop began asking about the work that they had bought as part of an estate.

It turned out it was indeed an important work, a painting by Willem de Kooning stolen 31 years ago from the University of Arizona Museum of Art and lost until Mr. Van Auker positioned it in a public place — lying on the floor of their shop in Silver City.

“Woman-Ochre”— one of a number of Abstract Expressionist paintings that Mr. de Kooning did of women in the 1950s — was stolen on the day after Thanksgiving in 1985. There was no surveillance video, but investigators pieced together a rough narrative of the theft that began with a man and a woman following a staff member into the museum around 9 a.m.

The woman distracted the staff member, while the man cut the painting from its frame with sharp blade. In less than 15 minutes, the two departed with the painting.