Software-based self-test (SBST) has recently emerged as an effective methodology for the manufacturing test of processors and other components in systems-on-chip (SoCs). By moving test related functions from external resources to the SoC's interior, in the form of test programs that the on-chip processor executes, SBST significantly reduces the need for high-cost, "big-iron" testers, and enables high-quality at-speed testing and performance binning. Thus far, SBST approaches have focused almost exclusively on the functional (programmer visible) components of the processor. In this paper, we analyze the challenges involved in testing an important component of modern processors, namely, the pipelining logic, and propose a systematic SBST methodology to address them. We first demonstrate that SBST programs that only target the functional components of the processor are not sufficient to test the pipeline logic, resulting in a significant loss of overall processor fault cove...