I don't know your turning skill level but here is something I do when I am turning straight sided boxes from face grain stock. Take a freshly sharpened spindle gouge, 3/8" or 1/2" depending on how far you have to reach over the tool rest and use it to cleanly cut the sides by taking fine shaving cuts along the sides of the piece. Keep the gouge sharp, hone the flute if necessary and gradually peel away wispy shavings until all the tear out is gone. Carefully control the cutting edge exposure so that only the smallest amount of material is being cut with each pass by gliding along on the bevel.
Tear out in end grain requires sand paper coarse enough to remove the "big" scratches left by the tool.
I may be getting a little older physically but mentally I'm still tarp as a shack.