  We explore the origin and orbital evolution of the Kuiper belt in the
framework of a recent model of the dynamical evolution of the giant planets,
sometimes known as the Nice model. This model is characterized by a short, but
violent, instability phase, during which the planets were on large eccentricity
orbits. One characteristic of this model is that the proto-planetary disk must
have been truncated at roughly 30 to 35 AU so that Neptune would stop migrating
at its currently observed location. As a result, the Kuiper belt would have
initially been empty. In this paper we present a new dynamical mechanism which
can deliver objects from the region interior to ~35 AU to the Kuiper belt
without excessive inclination excitation. Assuming that the last encounter with
Uranus delivered Neptune onto a low-inclination orbit with a semi-major axis of
~27 AU and an eccentricity of ~0.3, and that subsequently Neptune's
eccentricity damped in ~1 My, our simulations reproduce the main observed
properties of the Kuiper belt at an unprecedented level.
