We present a number of refinements of the Clearing Analysis on Phases method, i.e. the CAP method, introduced in the work of Doroudi et al. [1]. Namely, we show that the method can be adapted to calculate the elements of both the R and G matrices of special types of Quasi-Birth-Death (QBD) processes that frequently appear in the literature, and we also show how the method can be adapted to handle analogous types of QBDs with finitely many levels. Applications and connections to recent results/models from the literature will also be discussed.