The set of screened polarizabilities ᾱ j (iν), key quantities in the aforedescribed MBD@rsSCS model, are typically obtained by partial-contraction of the screened super-polarizability Ā(iν). We propose, instead, to first contract Dyson-like rs-SCS equation prior its iterative solution which directly provides the set of screened polarizabilities. This approach not only involves a reduced number of variables with the consequent reduction of memory requirements but also allows us to obtain screened polarizabilties in a linear-scaling fashion as it will be discussed profusely.