been looking for a compact scope with at least a 38mm objective. Is that a contradiction?

2-7
6x
1.5-6

I have 3 Vortex 6x scopes that are very sharp. they're about the same size as a 3-9

IMO yes.

If you drop your obj. req. down to 32mm then there are some significantly shorter scopes in 2-7 and that range. For instance Burris has one under 10 inches.

I understand your desire for a smaller compact scope. There is one potential issue however that I've run into... that is positioning the scope in the perfect position for ideal head placement. The compact scopes tend to have less relief and less mounting length before the front tube expansion. The combination of these often necessitates the scope being too far forward to get perfect positioning. I've never been a fan of off-set rings and if you're the same you may want to consider this if you're using a conventional length action. The one scope that is reasonably compact but offers good scope eye relief as well as tube length is the Leupold 6 power by 36mm front objective. These seem to work just fine. Good luck...

Both the leupie 6x36 and the 2.5-8x36 show as being 11.4 inches long. Both great scopes and you certainly have a point about head positioning with shorter scopes.