  We investigate a modification of the $k_\perp$-clustering jet algorithm for
hadron-hadron collisions, analogous to the ``Cambridge'' algorithm recently
proposed for $e^+e^-$ annihilation, in which pairs of objects that are close in
angle are combined preferentially. This has the effect of building jets from
the inside out, with the aim of reducing the amount of the underlying event
incorporated into them. We also investigate a second modification that involves
using a new separation measure. Monte Carlo studies suggest that the standard
$k_\perp$ algorithm performs as well as either of these modified algorithms
with respect to hadronization corrections and reconstruction of the mass of a
Higgs boson decaying to $b\bar b$.
