The Obey can be a very different river depending on conditions. If the gens are off and the Cumberland is running high, the Cumberland will backfill almost all the way to Dale Hollow Dam. Then you can run a Gheenoe whereever you want on no gens. It's almost like fishing stillwater though - very little flow. Usually I'll sight fish under those conditions - cruise around until I find a fish sipping midges and cast a small zebra midge to him and wait for him to find it. It's almost like bobber fishing.
On no gens with the Cumby low, the river will fall out fast and get very skinny. At that point you will be able to go downstream in your Gheenoe but you will have a hard time running up.
If one gen is on, you can fish streamers, but I wouldn't really do it alone. It's a narrow river with a lot of trees and boulders along the banks. If you get hung up or hook a big fish, you really need a second pair of eyes to watch where you're going for safety. A better choice might be to go to the lower end of the river and fish near the confluence for white bass and, um, other large fish that might be in there eating shad.
On two gens, it's not a safe river in my opinion - especially not forr fishing alone in a small boat. Go fish Dale Hollow or the Cumberland, or if you only have an hour or two to kill, you could wade the hatchery creek.
Wading access on the Obey sucks. On no gens, there is some access near the dam and at Moody's Ramp, but you can only really access a couple miles well by foot. A boat will get you to better fish.
Carry lots of midges because that's your forage base. If they aren't sipping midges, a small wooly bugger or a clouser dace with a lot of flash should get some fish.
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