In reply to GrahamD:
Of course it is up to you and your partners, although I wonder how many people would rap your lines if you told them that the knot would roll once and then tighten up just fine. I sure wouldn't; I want my knots to stay put when loaded.
As for complication, the shot I posted labeled "correct" is of a single overhand, but with the strands oriented so it doesn't roll, so no complication whatsoever there. For extra complication, I also posted a picture of the same knot with an additional overhand---but in only the small strand so very compact---that strangles off any possibility of rolling.
If I remember correctly, Moyers original tests suggested that rolling happened either sooner or more easily when the ropes were wet, so maybe you should test your setup that way too?