. - if you don't have any cleaning / painting / touch up work that needs completed in the apartment after the previous tenant moves out, let them in early.Pro-rate 8 days worth of rent and tell them that it'll be billed on their first rentalI would also get an addendum for the lease stating their new move in date, the pro rated rent amount, and have them sign it.

We managed to bump the rent up in our other unit from $825 to $995 with just cleaning/shampooing the carpets, appliances, and some touch-up paint.

The property from my initial walkthrough is in very good condition and beyond cleaning and some minor paint & touch ups, it should be a simple make-ready process.

Also easy to touch up when they move out..

Not sure how long they were there, but if it was a few years, hopefully you have paint to touch up the walls and I'd call that done. 

You should be able to patch the holes and touch up paint.

- If the house needs a small amount of touch-up paint, or some extra cleaning, how do you normally squeeze that in between the last day of the old lease and the first day of the new lease?

Properties that have been rented out for 5+ years tend to need a little more than a lock-change and paint touch-up before putting them back on the market.

Every turnover I touch up paint and have the units cleaned.

Some extra touch-ups to the property can enhance the value by attracting the renters.