Well I couldn't find a lot of good pics of dogwood up close but what I did find looks similar to this. I'll have to do a little more digging on that. Looks like it could be a a pretty desirable tree. Though it's like 2 inches from the patio so that's probably not a good place for it.

Daniel - Dogwood (Cornus) is just the beginning of the id process for your shrub. That is the genus but as yet we don't know the species. It could be a tree or a shrub. I have little knowledge of dogwoods but others here could probably give you a more precise name. But whatever it turns out to be, you are right, the position is not good.

This comment " . . . coming up around the patio in various places and also along the fence line," along with the reddish color of the branches implies to me that you should start by looking at the shrub dogwoods (such as Cornus sericea or C. stolonifera, red-twigged dogwood.)

Ok, I'll take a look at that. Shrub was my initial impression. I was out walking the fence in the back this morning and it's coming up in droves back there. I probably have 20 or more of them back there.

I get a lot of c. florida seedlings courtesy of the birds. There are five or six in my butterfly garden currently awaiting transplant.

Good point, Cecily. I guess that's a difference in where you are vs. where I am since I don't have enough C. florida around (only very few planted ones, none wild) to seed around much.

The comment that many are along the fence line implies that most are bird-planted regardless of whether they are shrubby or trees.

The Cornus Stolonifera looks like a likely candidate to me. I may need to wait till spring to to get a more positive ID. Thanks all for your input.