  Application of pressures or electron-doping through Co substitution into Fe
sites transforms the itinerant antiferromagnet BaFe(2)As(2) into a
superconductor with the Tc exceeding 20K. We carried out systematic transport
measurements of BaFe(2-x)Co(x)As(2) superconductors in pressures up to 2.5GPa,
and elucidate the interplay between the effects of electron-doping and
pressures. For the underdoped sample with nominal composition x = 0.08,
application of pressure strongly suppresses a magnetic instability while
enhancing Tc by nearly a factor of two from 11K to 21K. In contrast, the
optimally doped x=0.20 sample shows very little enhancement of Tc=22K under
applied pressure. Our results strongly suggest that the proximity to a magnetic
instability is the key to the mechanism of superconductivity in iron-pnictides.
