B757 Captain describes his inability to stay awake during a red eye flight and offers suggestions.

Narrative

During cruise; I was involuntarily falling asleep. I placed my seat in a reclined position and slept for an extended period of time. Flying all through the night and landing at 0845 domicile time cannot be accomplished with alertness without being relieved during cruise for a rest. Although the layover included a very long rest period; the attempt at taking a nap in the late afternoon in preparation for a red eye flight is often fruitless. Afternoon noise in the hotel as well as attempting to sleep during a period that does not fit my sleep cycle results in nothing more than 'toss and turn' for 3 or 4 hours. Provide a cruise relief officer and a rest station in the airplane; or officially allow and promote resting in the cockpit. Provide cockpit seats that facilitate taking a nap. Most of our 757's do not even have a head rest. Taking a nap in the pilot's chair is a painful experience. This aircraft had painfully hard seat cushions. Other solutions might be known and available in the industry.