The manifestation of miscellaneous aspect-oriented extensions raises the question of how these extensions can be used together to combine their aspectual capabilities or reuse aspect code across extensions. While white-box composition of aspect mechanisms can produce an optimal compound mechanism, as exemplified by the merger of ASPECTJ and ASPECTWERKZ into ASPECTJ 5, it comes with a high integration cost. Meanwhile, generic black-box composition can compose arbitrary aspect mechanisms, but may result in a compound mechanism that is suboptimal in comparison to white-box composition. For a particular family of aspect extensions, e.g., ASPECTJ-like mechanisms, glass-box composition offers the best of two worlds. Glass-box may rely on the internal structure of, e.g., a pointcut-and-advice mechanism, without requiring a change to the code of the individual mechanisms. In this paper we compare white-, black-, and glassbox composition of aspect mechanisms. We explain subtle composition issues using an example drawn from the domain of secure and dependable computing, deploying a fault-tolerance aspect written in ASPECTWERKZ together with an access-control aspect written in ASPECTJ. To compare the three composition methods, we integrate a TinyAJ extension with a TinyAW extension, and compare the results of running the aspects in a black-box framework and in a glass-box framework to the result of running these aspects in ASPECTJ 5.