The value of the critical temperature of the cuprates correlates with
the doping level and is affected by the interplay of two competing fac
tors: (1) the increase in carrier concentration, and (2) the pair-brea
king effect of magnetic impurities. An analysis of the temperature dep
endence of the critical field leads to the conclusion that magnetic im
purities are present even in a sample with the maximum observed value
of T-c. A new parameter, ''intrinsic'' T-c (T-c intr), which is its va
lue in the absence of magnetic impurities, is introduced. The maximum
value of T-c intr, which corresponds to the maximum doping level, appe
ars to be similar for different cuprates and to be equal to 160-170 K.
This is the upper limit of T-c in the cuprates.