Firewalls, key components for secured network infrastructures, are faced with two different kinds of challenges: first, they must be fast enough to classify network packets at line speed, and second, their packet processing capabilities should be versatile in order to support complex filtering policies. Unfortunately, most existing classification systems do not qualify equally well for both requirements: systems built on special-purpose hardware are fast, but limited in their filtering functionality. In contrast, software filters provide powerful matching semantics, but struggle to meet line speed. This motivates the combination of parallel, yet complexity-limited specialized circuitry with a slower, but versatile software firewall. The key challenge in such a design arises from the dependencies between classification rules due to their relative priorities within the rule set: complex rules requiring software-based processing may be interleaved at arbitrary positions between those where hardware processing is feasible. Therefore, we discuss approaches for partitioning and transforming rule sets for hybrid packet processing. As a result, we propose HyPaFilter+, a hybrid classification system consisting of an FPGA-based hardware matcher and a Linux netfilter firewall, which provides a simple, yet effective hardware/software packet shunting algorithm. Our evaluation shows up to 30-fold throughput gains over software packet processing.