Program restructuring techniques have proven successful in two-level automatically managed memory hierarchies. The possibility of extending them to multilevel environments is investigated. The performance of strategy-oriented restructuring algorithms in a three-level linear hierarchy managed by sampled working set policies or by a combination of sampled working set and local LRU policies is studied both analytically (assuming an independent reference model of program behavior) and by trace-driven simulation. The results of the study show that strategy-oriented restructuring may be as beneficial in a virtual memory with three levels as it is in one with two levels.