Depends on how long the span is, the shorter the span, the less the load, the shallower it can be set.  The longer the span, the greater the load from both weight and wind and thus the deeper it needs to be set.  

Unless it's an extremely short span (where you might even consider going without a pole except for height clearance issues) and unless you want to put guy wires on it, the deeper the better.  Or if you're putting this up where the wind blows or you have the chance of an ice storm, the deeper the better. 

And it also depends on your soil type.  I'd probably try to stay close to the same depth as the local REA goes, and try not to oversize the hole--diameter wise--too much, since it'll be pretty difficult to tamp the bottom of the hole back in solid.