Ian, a lot of it depends on how bad the stain is. If it is really bad then yes you have to remove the carpet because you will have to clean and treat the sub flooring and as you said you would have to treat the back of the carpet too..... UV lights are expensive if you buy them from a supplier of chemicals like most of us use, however they are only a few quid if you make your own..... At worse just buy a black light bulb and put it in the end of a lead, cost less than a fiver. You can get the bulbs from disco light places or at least in the US from almost anywhere, fancy dress places, joke shops, b and q. Maybe from a builders place you can get a light that has a clamp on it with a chrome or aly reflector, then just stick the bulb in and away you go, best, Dave.