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I have a U shaped pillow, but like you ended up on my back l. Ugh. I ended up getting a wedge shaped pillow that I use on my back to prevent myself from rolling over. Something like this:
Wedge Pillows for After Surgery Foam Wedge Sleeping Incline Pillow Bed Wedge Body Positioners Pregnancy Pillows 30 Degree Pressure Ulcer Back Pain Elevation Bolster Pillow https://www.amazon.com/dp/B08RSBMJRP/ref=cm_sw_r_apan_i_KDCV46RJ2DNX0XHPSSW6
If I do roll, then my one hip is still above the other hip so. Not completely flat.