When to list a rental unit with new purchase

[Michael Paling]

I'm currently under contract for my second duplex and I plan to move out of my first and into this next one. I'm wondering when I should start marketing the place that I currently live in for rent. Target closing date for duplex #2 is June 15, so I'd probably put an available date of July 1 on the unit I'm leaving. Should I be listing this place now or wait until after closing? I figure that I should wait till closing, but thought I'd ask here in case it's better to list sooner.