What do you mean by "Premium" seats? Are you booking the Premium Economy cabin, or are you looking for the "preferred" seats in Economy?
In any event, I believe that "preferred" seats are reserved for elites and those paying for the "Economy Delight" fare. Besides the obvious holding back of bassinet seats...
Preferred Seats
Preferred seats are available at an extra charge, so if you'd really like to secure a seat towards the front of Economy or Premium, this is the way to go.
Flying Club Gold, Delta Diamond and Delta Platinum members can select Preferred seats free of charge at any time, just make sure your membership number is added to your booking.