  We present numerical simulations to model the production of observable
long-period comets (LPCs) from the Oort Cloud, a vast reservoir of icy bodies
surrounding the Sun. We show that inner Oort Cloud objects can penetrate
Jupiter's orbit via a largely unexplored dynamical pathway, and they are an
important, if not the dominant, source of known LPCs. We use this LPC
production to place observationally motivated constraints on the population and
mass of the inner Oort Cloud, which are consistent with giant planet formation
theory. These constraints indicate that only one comet shower producing late
Eocene bombardment levels has likely occurred since the Cambrian Explosion,
making these phenomena an improbable cause of additional extinction events.
