Background. Function Point Analysis is the most used technique for sizing software functional specifications. Function Point measures are widely used to estimate the effort needed to develop software, hence the cost of software. However, Function Point Analysis adopts the point of view of the end user, and –consistently– considers a software application as a whole. This approach does not allow for assessing the role of reusable components in software development. In fact, reusing available components decreases the cost of software development, but standard Function Point measures are not able to account for the savings deriving from component reuse. Objective. We aim at modifying the definition of Function Point Analysis so that the role of components can be taken into account. More specifically, we redefine the measurement so that when no components are used the resulting measure is the same yielded by the standard measurement process, but in presence of components, our modified measure is less than the standard measure (the bigger the role of components, the smaller the measure). Method. Components partly support the realization of elementary processes. Therefore, we split elementary processes into sub-processes, such that each sub-process is either totally supported by a component or it is not supported at all by any component; the size of the elementary process is defined to be inversely proportional to the size of sub-processes supported by components. Results. The proposed approach was applied to a Web application, which was developed in two versions: one from scratch and one using available components. As expected, the 'component-aware' measures obtained are smaller than the standard measures. We also compared the reduction in size with the reduction in development effort. Conclusions. The proposed method proved effective in taking into account the usage of components in the development of the considered application. However, the observed decrease in size is smaller than the decrease of development effort. The latter result suggests that this initial proposal needs further experimentation to support accurate effort estimation.