Volunteered Service Composition (VSC) refers to the process of composing volunteered services and resources. These services are typically published to a pool of voluntary resources. Selection and composition decisions tend to encounter numerous uncertainties: service consumers and applications have little control of these services and tend to be uncertain about their level of support for the desired functionalities and non-functionalities. In this paper, we contribute to a self-awareness framework that implements two levels of awareness, Stimulus-awareness and Time-awareness. The former responds to basic changes in the environment while the latter takes into consideration the historical performance of the services. We have used volunteer service computing as an example to demonstrate the benefits that self-awareness can introduce to self-adaptation. We have compared the Stimulus- and Time-awareness approaches with a recent Ranking approach from the literature. The results show that the Time-awareness level has the advantage of satisfying higher number of requests with lower time cost.