Melatonin and trazodone worked for me. In early sobriety I'd take sleeping on and off all day over the alternative. I did medical detox from alcohol and Lunesta cross addiction using a benzo taper, which worked wonders.
Very glad to be done with all of it. When in active addiction I took 3 mg of lunesta without fail every night, the max dosage. And doxylamine succinate (Unisom). And 10 mg of melatonin. And 200mg of trazodone. All this after drinking at least 3 glasses of wine on a slow day.
I still have a hard time sleeping on nothing. I'm at 1-2 mg of melatonin and 25 mg. of trazodone most nights, but my sleep is HUGELY restful. Now the unisom makes me feel really anxious and groggy when I wake up, as does any more of anything. The worst for me was valerian root. But different things work for different people.
I come by it honestly, I come from a long line of insomniacs. I agree with everyone suggesting natural methods, but some "help" is not out of the question in withdrawal, particularly if you have a doc that can advise you honestly.