Flat Head Syndrome

My 1 month old son always sleeps with his head turned to the left at night and the back of his head on that side is becoming flat. I tried propping his left side up with a blanket that way the weight of his head would fall the the right side, but he still manages to turn back to the left. I also don’t want to have him sleeping with the blanket in the bassinet while I’m sleeping. Does anyone have any suggestions on what I could do? He has very strong neck muscles, gets plenty of tummy time, and can easily move his head around, but favors laying with his head turned to the left while sleeping.