Bagger, you don't say what your 'normal' tuning is. If it's EADGBE, then the 'C' tuning is way lower and the reduced tension wil allow the neck-relief to set back somewhat, and that will effectively lower the action and make for string-rattles.

I have two guitars, one which I use predominantly for 'standard' and Drop 'D', and the other for 'low' tunings such as DADGAD, 'C' and 'C' Modal, and they are set up accordingly.

If you're in the UK, you might try ordering some 'C' strings from Malcolm Newton - www.newtonestrings.com - he'll make them in your normal gauges and the tensions will be the same as for a 'standard' set in standard tuning EADGBE - so they will 'feel' exactly like a 'standard-tuned' guitar. They're hand-made and not especially expensive, but there is a minimum order quantity - not sure what it is.