Removing one bulb indicates that they are wired in series. I have NEVER heard of any lights in a house being wired in series except Christmas tree strings. If it was done by an electrician then he should call a different electrician. It does not sound correct.
Perhaps if some info on the fixtures could be provided that would help. Info on how they were wired would be helpful also but I doubt that is available if not done by the OP.
The most common mistake with three ways and multiple lights is taking a drawing with one light between the switches and trying to do it multiple lights. It is not realized that four wires are needed and not 3 wires to make it work properly. The light end up in series and are dim when turned on. This is what I was suspecting.
Last edited by JoeD; 03-01-2013 at 06:14 PM.