When booking a weeklong yoga retreat, Amanda Levy signed up for a special package. Called "digital detox," it promised a 15% discount if Ms. Levy, a sales executive at a San Francisco social-networking company, would agree to leave her digital devices behind, or surrender them at check-in.

"I am constantly on my iPhone and checking my email," says the 29-year-old, who admits she sometimes "feels naked" without her smartphone. "But it was nice to be able to shut it off. It gave me an excuse to feel OK about not checking in."

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