  Low-mass binary millisecond pulsars (LMBPs) are born with very small orbital
eccentricities, typically of order $e_i\sim10^{-6}$--$10^{-3}$. In globular
clusters, however, higher eccentricities $e_f\gg e_i$ can be induced by
dynamical interactions with passing stars. Here we show that the cross section
for this process is much larger than previously estimated. This is because,
even for initially circular binaries, the induced eccentricity $e_f$ for an
encounter with pericenter separation $r_{\rm p}$ beyond a few times the binary
semi-major axis $a$ declines only as a power-law, $e_f\propto(r_{\rm p}/a)^
{-5/2}$, and {\it not\/} as an exponential. We find that {\it all\/} currently
known \lmbps in clusters were probably affected by interactions, with their
current eccentricities typically an order of magnitude or more greater than at
birth.
