Will Lowering The Dosage Of Nature Thyroid Cure My Insomnia?

I take Nature Throid 65 mg 2 x a day and my latest levels were tsh 0.02, T4 - 7.9, T3 31.0%. I was feeling fine - hair thicker, nails stronger, better energy, dry eyes better, etc. Only problem is insomnia. My family doctor has lowered the dose to 32 mg a day. Does this sound reasonable?