  We present a scenario for the spin-up and evolution of binary millisecond
pulsars. This can explain the observational properties of the recently
discovered binary millisecond pulsar PSR J1740-5340, with orbital period 32.5
hrs, in the Globular Cluster NGC 6397. The optical counterpart of this system
is a star as luminous as the cluster turnoff stars, but with a lower Teff (a
larger radius) which we model with a star of initial mass compatible with the
masses evolving in the cluster (~0.85 Msun). This star has suffered Roche lobe
overflow while evolving off the main sequence, spinning up the neutron star to
the present period of 3.65 ms. There are evidences that at present, Roche lobe
overflow is still going on. Indeed Roche lobe deformation of the mass losing
component is necessary to be compatible with the optical light curve. The
presence of matter around the system is also consistent with the long lasting
irregular radio eclipses seen in the system. We propose that this system is
presently in a phase of `radio-ejection' mass loss. The radio-ejection phase
can be initiated only if the system is subject to intermittency in the mass
transfer during the spin-up phase. In fact, when the system is detached the
pulsar radio emission is not quenched, and may be able to prevent further mass
accretion due to the action of the pulsar pressure at the inner Lagrangian
point.
