Yep, the pad needs to be snugged up against the tender bits. I went on a 50-ish-mile group ride last weekend, after not riding more than just a few miles at a time this whole year. I was concerned about chafing that was occurring at this rather sensitive point, with some Assos shorts that were not yet broken-in, and thought I might have to discreetly end the ride early, but at the first potty break, at 13 miles, I made sure the pad was snug, and the problem ended. The shorts were not in need of break-in; I just had to snug them up right.
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