That'a a great response from Lugnut. Cleared up a few points for me, like the lower limit of the vibration control of my LP12's suspension. Thanks Pat!
Just to add my 2 cents... a wall shelf is one of the best ways to mount a suspended TT, IF the wall is an outside, structural, load-bearing wall. Such a wall is coupled directly to the ground. My LP12 is mounted like this and you can slam the front door ( a few feet away behind an interior wall ) without the turntable noticing it.
RF Sayles, you've made it clear that your TT shelf is not mounted on such a wall. Your short wall may be coupled to the floor in that case, and if the floor is at all bouncy then low-frequency, seismic-type vibrations are reaching your TT's suspension and it cannot deal with these effectively. Really, nothing much can that I know of, although the roller bearings others mention might be something to try.
In my experience, if the floor is at all bouncy, a heavy floor-mounted support is not a viable alternative to a properly set up wall shelf. I once worked in a first-floor store which demo'ed TTs ( yes, long ago ) on a low brick wall. Real brick, and quite deep. The thing looked solid, but if you walked by with a heavy tread you could see ( and feel ) the whole wall oscillate very slowly up and down, at maybe 1 or 2 Hz. Lugnut's suggestion of a support pillar under your short wall ( down in the basement, if you're listening on the first floor ) makes excellent sense. Channel the load on the shelf down to the ground and you've got a sink for vibration.
Or you could just move the TT shelf to an outside wall, thus necessitating a rethink of everything else in the room as well... not an option, perhaps!
Finally, Linn's Trampolin suspension is said by some to be useful if your TT support transmits vibration, but others say it does not help the sound. I have removed mine, and I run my LP12 on a Target wall unit with the standard shelf and Audio Technica feet.