60 Cylce Hum Driving Me Batty

I have a circuit which takes a 15VDC supply from a wall adapter.
Most connections are made by shielded cables and I have employed the manufacturer's (and others) recommendations for hum reduction.
Is it possible to insert a 60-cycle notch filter or other high-pass that'll attenuate the hum?
 
Have you tried a different wall wart? Some are better than others. What current rating does it have?
It could even have a half wave rectifier and very little capacitance, if the noise really is 60hz.
A simple filter won't work.
 
The noise voltage may be common mode and a filter will have little effect. The worst offenders are switch mode supplies that lack a "safety ground". This leaves half the line voltage (~60VAC @60Hz) on both + and - outputs with respect to earth ground. The "safety ground" on switch mode supplies is the return path of the line filter, and if it is open, then the line filter is a capacitive divider that leaves half the AC line voltage on the DC output. Grounding one side of the DC output may help.