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In this work we present a second s-z mapping (ST2) as an extension of a first one, the s-z mapping (ST1), presented in a previous work done by the authors. In that work, the ST1 mapping used only one tuning parameter (csi) ξ to: 1) map the (asymptoticall stable) left half s plane in the interior of the unitary circle in z plane; and 2) attain the asymptotical stabilization of a benchmark harmonic oscillator driven by a PD discrete controller with various sampling periods. In both tests, the ST1 mapping behaved better than other mappings listed in the literature (Tustin, Backward, Shneider-Kaneshige-Groutage, etc.). In this work we use two tuning parameters csil and csi2 in the ST2 mapping to see how both tests behave, including numerical simulations comparing the ST2 mapping with those other mappings ((ST1 and Tustin).