Modern network processors (NPs) increasingly deal with packets with heterogeneous processing requirements. In this work, we consider the fundamental problem of managing a bounded size buffer at the input queue of an NP. Incoming traffic consists of packets, each packet requiring several rounds of processing before it can be transmitted out of the queue. The objective is to maximize the total number of successfully transmitted packets. In such an environment, it is well known that Shortest-Remaining-Processing-Time (SRPT) first scheduling with push-out is optimal [1]. However, it is hard to implement both priority queueing (PQ) by remaining processing and the push-out mechanism simultaneously in an NP. We explore alternatives for this architecture, addressing the simplicity vs. performance system design tradeoffs. We design a simplified architecture and provide worst-case guarantees for its throughput performance in different settings. We also conduct a comprehensive simulation study that validates our results.