The unpredictable fluctuations in computing resources, contexts, and user preferences that characterize pervasive environments have stressed the need for context-aware self-adaptive systems. So far, this research area mostly dealt exclusively with concerns related either to standard QoS or to security. Taking into account trade-offs between these two conflicting concerns is a key issue, since they both compete for the same resources. This paper presents a general adaptivity model that reconciles these two concerns. This model is formalized as a component composition selection process, where the best composition is found by reasoning on security and non-security properties of the system. Utility functions are used to quantify how a component composition alternative is appropriate in a given context, with respect to the user preferences.