Do smaller apertures give slightly sharper detail? (24-70)

Generally speaking, is it fair to say that lenses are sharper at smaller apertures than wider apertures, with both focused on the same focus point? I don't mean depth of field -- I mean a detail that is "in focus" at both f/2.8 and f/8 -- but at 100% crop, the f/8 detail is slightly sharper than the 2.8 sample. I'm noticing this on my 24-70L after shooting various subjects using center focus point, tripod, mirror lock up, and timer. I'm enjoying the lens and I suspect this might just be the nature of lenses.

The difference is probably a bit more distinct when using the telephoto (70mm) end.

A comparison sample at the digital picture.com also seems to confirm this (roll over image to see comparisons):

http://****/ys5swz

Thoughts and insight?

Lens quality gets better when stopped down a bit. The optimum aperture is mostly about two to three stops closed, depending on the lens. After that, diffraction kicks in, and things get less sharp again.

Most lenses are slightly softer wide open at their maximum aperture, get a little better to about f/8 and then get softer due to the effects of diffraction caused by the small aperture hole when the aperture gets smaller than about f/11.

However, every lens is different so you have to test you own lenses.

Thanks guys.... your comments confirm what I have been reading. Thanks a bunch