Good cables are a must for noise reduction as well.
One other thing you could check out is a possible Ground-Loop. Try different Outlets in search for a isolated circuit with a full 120v current needed for most Amps in North America (A lot of recent players have plugged into 120v and fryed their Vintage Amps because in the 60's the US Standard current was 110v and they didn't know the older amp needed to go through a Variac).
A looped circuit is where other componants (like a TV) also draw from the same amperage as your amp draws from and will cause interference.
Isolated Circuits are one of the most important specifications dedicated to the Recording Industry Today.