WHEN TERRA and Mark Osterling divorced, they faced a question common among older couples: Can we share custody ... of the dog?

The answer is yes. The upstate New Yorkers worked with a mediator to draw up an agreement spelling out expectations for their mixed breed: Neither will withhold access to Willy without due cause. They’ll collaborate to provide primary care in the event of his illness or injury. If one travels, the other will take over Willy’s care—and will not pass on that care to an unapproved third party.

DanaMarie Pannella, an associate attorney in Sharon Center, Ohio, says some couples don’t wait until divorce; they draw up custody arrangements when they get the pet. She calls such an agreement a “pup-nup.” —Robin L. Flanigan