  We report comprehensive resistivity measurements of single crystalline
samples of the Ba(Fe(1-x)Co(x))2As2 high Tc superconductor under hydrostatic
pressure up to 2.75 GPa and over a broad concentration range, 0 < x < 0.099. We
show that application of pressure progressively suppresses the SDW transition
temperature, T_SDW, in the underdoped regime. There is no sign of
pressure-induced superconductivity in the undoped BaFe2As2 down to 1.8 K, but
applied pressure dramatically enhances Tc in the underdoped regime. The effect
of pressure on Tc is very small in the optimally and overdoped regimes. As a
consequence, the dome of the superconducting phase extends to x 0.02 under
pressure. We discuss the implications of our findings in the context of a
possible quantum phase transition between the SDW and superconducting phases.
