It's all about building relationships. There are always trees that a service removes that no mill will accept. We have done this for so long that a few tree services now just assume we'll take there scraps and drop them off without us even asking. My partner got home from our hard day of pine clearing to find that a tree service had dropped 3 full dump loads of oak and hickory limbs and trunks in his yard. They left a business card so he would know who dropped it. We have only gotten "trash wood" (pine / sweetgum) once like this and when I called to complain, they came back out with a grapple truck and loaded it and hauled it away. The next week, they brought twice as much oak as a "peace offering"... LOL. I'm headed to my partner's house in a few minutes to start working up what was dropped there yesterday.
Remember... you are providing a benefit to the tree services when you give them a place to dump the wood nobody else will pay for.