Hum from Florescent light

Gmkowal(or anyone else...) do you know of any other fixes for this problem. I have recently gotten some new equipment(interconnect/power cords/CD player), and encountered the problem. No flourescent lights. Just the interconnects picking up the 60 Hz AC hum from passing by a power cord. I know the best solution is to rearrange the equipment to minimize this. I am not jumping for joy to do this, as my current arrangement is good(by that I mean my girlfriend wants it this way...). Temporarily, I have found that pulling my interconnects as far from the offending power cord as is possible, mitigates the problem to a large extent. But NOT completely. But, I am wondering if there are any other solutions out there. Never experienced these gremlins before. But, I guess that's life. Thanks to all in advance.

Thanks to all for the suggestions. I can see there are lots of people on this site smarter than I. Some of my interconnects have no shielding, so I cannot vary that. But, I did try reversing them. I have many interconnects, and have found the problem was only ameliorated(not completely) by a pair of Monster(I know, I know...) cables. And, I think that is because they are two meters. I can keep them away from the power cord. That's how I realized the others should be kept away from the cord. I have tried Coincident, AudioQuest, HomeGrown Audio(2 of them), Tara, Kimber(not sure why - same as HGA, maybe desperation), and Monster. I haven't heard any of the new Audioquest line, but they could be better in this area than their old line. I am not sure, thought they only changed surface quality of their metals, cosmetics, plugs, and PRICES. I would like to stick with the Coincident and Home Grown Audio if at all possible, as they do things I really love. Thought about the grounding connection on my integrated(not using a preamp these days) a long time ago. When I first started having these problems. I should do it right this time, last time I didn't give it much effort. I blamed the HGA products/RFI. RFI blockers helped, but now I realize my problem is AC. Will try the grounding suggestion. A thousand thank yous. Joe.