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It is shown that only a part of contributions in the full expression for the (amputated) two-leg graphs in effective single-scalar S-matrix theory can be considered as the self-energy function. This part is uniquely fixed by two requirements: the correct wave function normalization and the true (physical) position of the 2-leg Green function pole. On the one-loop level there is no need in fixing the other unknown constants because they turn out absorbed by the parameters that appear only in one-loop S-matrix graphs with n ≥ 3 legs. This means that the problem of fixing the dimensional coupling constants turns out shifted to the next stage of the renormalization procedure. Also, it is shown that the same is true with respect to the multi-component effective scalar theory. In this case the requirements of diagonalizability and correctness of pole positions turn out sufficient for one-loop renormalization of two-leg S-matrix graphs. [ABSTRACT FROM AUTHOR]