A Star is Born 'Jackson Main' Real Acts Like This

[Mykesbass]

OK, bit of a convoluted title, but watched the Bradley Cooper/Lady GaGa film the other night. Although not the greatest performance (but pretty good for an actor), I did like the style of music that Bradley Cooper was playing - a sort of heavy Country tinged Rock/Blues. 

I thought of Chris Stapleton - but that's too Country. The nearest I have found is a bit older, and not as heavy in Delbert Mc Clinton.  

Can anyone recommend anything similar - riff based, but with a bit more structure and more interesting songwriting than most of the Blues/Rock that I know. Thanks.