Implementors of message-passing libraries have focused on optimizing point-to-point protocols and have largely ignored the performance of collective operations. In addition, algorithms for collectives have been tuned to run well on networks of uni-processor machines, ignoring the performance that may be gained on large-scale SMP's in wide-spread use as compute nodes. This is unfortunate, because the high backplane bandwidths and shared-memory capabilities of large SMP's are a perfect match for the requirements of collectives. We present new algorithms for MPI collective operations that take advantage of the capabilities of fat-node SMP's and provide models that show the characteristics of the old and new algorithms. Using the Sun^TM MPI library, we present results on a 64-way Starfire^TM SMP and a 4-node cluster of 8-way Sun Enterprise^TM 4000 nodes that show performance improvements ranging typically from 2x to 5x for the collectives we studied.