Oscar-winning film and stage director Sam Mendes saw his Broadway stage revival of "Gypsy" (starring Bernadette Peters) get completely shut out at the Tony Awards Sunday night, but he can seek some consolation from his wife, "Titanic" star Kate Winslet.

That's right -- we said wife. The filmmaker and the actress were recently married, a publicist for the couple finally confirmed Monday.

"This is to formally announce that Sam Mendes and Kate Winslet married in late May in a very small ceremony whilst on holiday in the West Indies. ... Present were Kate Winslet's (2 1/2-year-old) daughter, Mia, and three close friends," the rep said in a statement.

This marks Winslet's second marriage, following her 2001 divorce from her husband of three years, film director Jim Threapleton, whom she met on the set while the two were making the indie feature "Hideous Kinky." The pair had daughter Mia together, but the relationship eventually crumbled.

Mendes's movie credits include 1999's "American Beauty," for which he received the Best Director Academy Award, and last year's "Road to Perdition." Before meeting Winslet, he was linked with such actresses as Rachel Weisz, Jane Horrocks and Calista Flockhart.

But it was shortly after her divorce that Winslet, 27, and Mendes, 37, quietly began going out together, first appearing in public at the New York premiere of her movie "Iris" in late 2001.

"He's a good man," Winslet told PEOPLE at the time. "You can say I said that with a large smile on my face."