Can you give me advice on trimming a cedar tree?

I have a cedar about three stories high on my property next to my neighbors' property line. Their cable and electric wires run through it at a little lower than the one story mark -- they got the electric co to trim some branches without my knowledge and then the neighbor was out there doing it, and saw him and stopped him because it IS my responsibility. He said he was calling his cable co. to see what they had to say about trimming close to their wires. Frankly, I think their concern is foolish because none of those branches could pull their wires in a storm, the only thing would be if the whole tree came down (it's alive and healthy) and that would take out wires from about four houses, including my own. But to keep peace in the neighborhood, tell me -- will denuding the tree of branches up to and maybe just past a story make the tree too top heavy and make it more likely to come down in a storm? I would hate to have to cut it down for so many reasons, ecological and financial, but if it's the only proper thing to do, it would have to be done. Any advice, very much appreciate.