A parallel computer includes nodes that include a network adapter that couples the node in a point-to-point network and supports communications in opposite directions of each dimension. Optimized communications include: receiving, by a network adapter of a receiving compute node, a packet—from a source direction—that specifies a destination node and deposit hints. Each hint is associated with a direction within which the packet is to be deposited. If a hint indicates the packet to be deposited in the opposite direction: the adapter delivers the packet to an application on the receiving node; forwards the packet to a next node in the opposite direction if the receiving node is not the destination; and forwards the packet to a node in a direction of a subsequent dimension if the hints indicate that the packet is to be deposited in the direction of the subsequent dimension.