We discuss classical arguments leading to the theoretical death-line o
f radio pulsars. We show that the consideration of an additional const
raint on the one-photon e+/- pair creation in the presence of a strong
magnetic field, namely that the electron energy sufficient to trigger
this process does not exceed the maximal energy set by the balance be
tween the electron acceleration and cooling rates, yields an additiona
l death-line. This extra line is significantly flatter in the P-P plan
e than the usually invoked death-line and becomes relevant for short-p
eriod pulsars (P less than or similar 0.1 s). We discuss briefly the l
ikely enhancement of the one-photon e+/- pair production rate due to t
he presence of rotation-induced electric fields and its influence on t
he slopes of both death-lines. When shifted to fit observations of mil
lisecond pulsars, this additional death-line nearly coincides with the
Hubble limit. Millisecond pulsars are thought to be recycled pulsars,
spun up in binary systems, and thus cannot be subject to restrictions
imposed by the finite age of the Universe. We therefore attribute the
ir absence below the line of the Hubble limit to the presence of this
additional death-line.