In a small bowl, combine mayonnaise, 1 tablespoon chives, and lemon juice. Add crabmeat; stir with a fork to combine. Season with white pepper and salt.

Spread one side of each slice of bread with butter. Arrange avocado slices on half of the buttered bread slices. Top with crab mixture. Add watercress. Top with remaining bread slices; buttered-side down. Trim the crusts from bread. Cut each sandwich into 3 equal pieces. (Sandwiches can be filled and refrigerated, covered tightly with plastic wrap, for one hour before serving.) Garnish with additional chives before serving. Makes 12 small sandwiches.