08/25/2008 at 01:00 AM EDT
During a surprise fireworks display at the Cove Atlantis (a gift from the resort), "we danced and held hands," says Jewel (in a Monique Lhuillier gown). The very private affair—only pals Jason Freese, who officiated, and his wife, Amy, attended—"was picture perfect," says Ty.
Why elope? "That's what marriage is," says Ty, "just me and her." But, adds Jewel, "we're ready to start a family."
Jewel found the cowboy-and-bride cake topper online; Lorraine Schwartz designed the couple's rings (inset).
After calling their families to break the news, the couple dined on Bahamian lobster and chocolate bento boxes.
Jewel, 34, and Murray, 38, who've dated for 10 years, wrote their own vows. "Neither of us cried," says Jewel. "We were happy!"