We report a combined study of external pressure and Cu-substitution on BaFe2As2 single crystals grown by the in-flux technique. At ambient pressure, the Cu-substitution is known to suppress the spin density wave (SDW) phase in pure BaFe2As2(T(SDW) ≈ 140 K) and to induce a superconducting (SC) dome with a maximum transition temperature T(c)(max) ≃ 4.2 K. This T(c)(max) is much lower than the T(c) ∼ 15-28 K achieved in the case of Ru, Ni and Co substitutions. Such a lower T(c) is attributed to a Cu(2+) magnetic pair-breaking effect. The latter is strongly suppressed by applied pressure, as shown herein, Tc can be significantly enhanced by applying high pressures. In this work, we investigated the pressure effects on Cu(2+) magnetic pair-breaking in the BaFe(2-x)Cu(x)As2 series. Around the optimal concentration (x(opd) = 0.11), all samples showed a substantial increase of T(c) as a function of pressure. Yet for those samples with a slightly higher doping level (over-doped regime), T(c) presented a dome-like shape with maximum T(c) ≃ 8 K. Remarkably interesting, the under-doped samples, e.g. x = 0.02 display a maximum pressure induced T(c) ≃ 30 K which is comparable to the maximum T(c)'s found for the pure compound under external pressures. Furthermore, the magnetoresistance effect as a function of pressure in the normal state of the x = 0.02 sample also presented an evolution consistent with the screening of the Cu(2+) local moments. These findings demonstrate that the Cu(2+) magnetic pair-breaking effect is completely suppressed by applying pressure in the low concentration regime of Cu(2+) substituted BaFe2As2.