Can you provide some voltage figures for:
idle, no lights
5000 rpm, no lights
idle, lights
5000 rpm, lights
generally, the voltage should stay between 13 and 14.5 volts if the reg/rec is doing its job correctly. How old is the battery, may I ask? you can get that tested for efficiency aswell to see if its ok
you may have a dud battery (it happens) but chances are its not