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How do I maintain upper-back tightness while bench pressing?

You know, that was an issue that I'd had/been having as well. The one thing I can say about it is that I’ve had to make a conscious effort to activate the lats before I bench and make sure (along with my lower half) that I work to keep my muscles flexed when I bench

Video credits to Gaglionestrength. It directly answers the question you've asked.