How to handle overlapping leases?

[Kathryn Pierce]

My short term tenant vacated 2 weeks early (on good terms). Which worked out well because the new long term tenants wanted extra time to move-in. 

I can do an addendum to the new tenant's lease and charge them pro-rated rent for August, but how do I handle the existing tenant's lease? Technically they have the unit until August 31st. Do I do an addendum to their lease, and provide them all of the prorated rent from the next tenant? Is it fair to keep a portion of the prorated rent for the extra paperwork I'm doing? 

Also, the short term tenant was paying a higher rate. So if I was truly prorating their August rent, I'd owe them money. 

This works out well for everyone, but I just want to make sure I'm doing this legally. Thanks!