What to do when removing limits doesn't work (or isn't enough) on a prefabbed pose?

This has bothered and baffled me for a while: quite often--in fact nearly always--I'll want to tweak a prefabbed pose, but on making adjustments find that e.g. the eyes I see staring straight ahead are cranked all the way over to the left...at least according to the slider. So I disable limits, but the eyes refuse to swivel much farther, and certainly not as far as they can and should.
The same happens with joints, limbs, and digits, and I'm wondering what the cure is. There must be a way to defeat this artificial limit-within-a-limit.
As always, any advice will be appreciated.
Comments
I've seen something similar to this myself a few times. My first guess (using the eye position as an example) would be to first zero the eye position in Pose Controls, then select each eye itself individually and look at the parameters tab. If the values are not zero, simply zero them out and the eyes should be fine. Quite often, pose creators will position the eyes without the use of the "Eyes Left/Right" slider in the figure's pose control.
Hope that helps!
Are you using the transforms on the bone itself or are you working with the Pose Controls on the figure?
As a relative novice, I'm not sure I understand the difference. Usually I select the character, go to Pose Controls, select the part I want to tweak, and use the sliders provided. Is there another, better way?
Those are "remote controls" for the actual rotation sliders on the body parts. Remove Limits affects the body parts but not the Pose Control sliders, so depending on how they are set up you will see no or little difference. If you select the eye itself, with Limits off you will be able to make it rotate freely.