We propose that the transition temperature in the layered cuprates is
affected by a peculiar interplay between doping and pair-breaking scat
tering. This scattering can lead to a depression of T-c relative to it
s ''intrinsic'' value. Using this picture, one can explain the large v
alue of T-c in the three-layered cuprates relative to the two- and one
-layer cuprates and also understand the large pressure effects observe
d. We predict that one can raise T-c above the usual maximum value by
applying pressure on underdoped TI-2201 samples and the maximum value
of T-c under pressure is evaluated. The temperature dependence of the
pressure coefficient is also discussed.