Neoprene brace for sports injury: Compression vs. circulation

Neoprene braces are commonly available for injuries e.g. for elbow,
wrist, knee, and ankle. Ostensibly, it provides compression (to reduce
swelling) and keeps the joint warm. My impression was that you want
cold compress within the first 2 days of the injury to prevent swelling,
then warmth afterward to improve circulation. My question is: Wouldn't
less compression improve circulation? Or is the compression from the
brace far outweighed by the warmth? Thanks.
.

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