Hi all - I've wanted to get a GSP for the better part of a decade to serve as a hiking buddy/all around dog and finally took the plunge with Rudiger, a ~2yo rescue dog.

He's still in his first week with my family and there have been a few instances where he initiates a gentle, almost purr when being petted on a couch/bed. If petting continues he'll escalate the tone and growl. One time he reached back quickly and put his mouth around my arm with virtually no pressure, but he definitely seemed irritated. When I stopped petting his shoulder he promptly got up, turned around and nestled up to rest on my leg. He usually doesn't react that way again if petted shortly after it occurs, unless you hug him which seems to make him uncomfortable.

Another instance of growling was on my bed and my 13yo english black lab female hopped up, he growled at her. She very rarely jumps up on the bed but seems to be more interested now that Rudi is a regular fixture on the furniture.

This is the only area of his behavior that has been of concern as he gets considerable exercise, comes when called, is very well behaved off leash in unfenced areas (with Layla my lab and toys/treats to keep him engaged) and spends a lot of time wagging his tail and being affectionate towards me and playful with Layla.

I'm looking for guidance on how seriously this behavior should be taken on my end and the best course of action going forward. My hunch is that he was treated poorly at some point, is just not used to a lot of affection or needs time to adjust to living with another dog. At the upper end of the spectrum I'm thinking he needs to be carefully trained/taught that he is not in charge and that he needs to act appropriately in the house.

To work on the dominance issue I've been running him on a front point harness to keep him level or behind, ensuring he sits prior to getting any food or treats, etc.

Sorry for the wall of text, hopefully this is the right amount of information for you to make informed comments. 

 No couch and bed rule is in effect. Rudi isn't a fan of it and he gave a little growl the third time I got him off the couch. After firming up my voice and giving him a light pull on the shoulder he came down and curled up on his new dog bed.

Thanks for the advice, he definitely has a little dominance issue that needs to be addressed.

Tonight was the first night he was given the option to go out and run in the yard around 8pm and he opted to stay inside. It's good to see him finding his exercise/rest balance . He was really good today at sitting, shaking and running at my side. Here he is with Layla:

Took Rudi out for a weekend of winter camping. He was off leash in a wooded area for the better part of two days, stayed within 100 yards about the whole time, dug about 50 holes under tree stumps and fallen logs, and wasn't bothered by a variety of gunshots ranging from .22 to .50 rifles and shotguns.

He's warming up quickly to the family and has been compliant with getting bathed, having his paws cleaned and trips into town to the pet store. His discipline is improving each day with a very positive training regimen of treats and encouragement for listening to commands. He loves making new friends, canine and human.

After a few days he's learning to stay off his favorite couch and is perfectly happy to sleep in his crate and in the laundry room when unattended. Couldn't be happier with his response to training and eagerness to learn the "rules of the pack". Now if I can only get him to add a few pounds to get to 60-65lbs he'll be in great physical shape. He runs tirelessly and is eating ~5.5 - 6 cups a day plus several veggie treats. He might need to go up to 7 cups in order to get to a healthy weight, we'll see how it goes.

Anyone else have to feed more than 6 cups/day in order to put healthy weight on a GSP? Rudi is a good sized male recovering from pneumonia in November where he was close to not making it. He's up to 52lbs now but is still bony.

Here he is sitting for grandma: