I am also renting in June, and have already booked a car. This is through National, I belong to their program. The good thing are... I don't have to pay anything now. If a better price comes up, I can modify for that... and I'm guaranteed to have a reservation.
I would book now and then modify or cancel as you get better deals.
ETA: Paying $44.50/day for a Standard car. I'm doing two "one-way" rentals.