In a large oblong pan or dish:
Layer 1: Spread one head broken up lettuce.
Layer 2: Combine and spread 1 cup chopped onion and 1 cup chopped green pepper.
Layer 3: Spread 1 (16 oz.) can (chilled) drained small sweet peas.
Layer 4: Spread 1 pint or more mayonnaise (not salad dressing) over peas.
Layer 5: Sprinkle 3 tablespoons sugar over mayonnaise.
Layer 6: Crumble 1 pound crisply fried bacon and spread over sugar.
Layer 7: Top with 1 pound finely grated cheddar or American cheese.
Wrap tightly with plastic wrap and chill overnight. Serves 10 to 12 generously.