Integrated IP over wavelength division multiplexed (WDM) networks with generalized multi-protocol label switching (GMPLS) capabilities are a promising candidate for the next generation optical Internet networks. By using a unified control plane, such networks efficiently utilize resources both at the IP layer and the WDM optical layer. In an IP/WDM network, IP routers are connected to wavelength cross-connect (WXC) switches through wavelength ports (or ports). A port requires an optical transceiver and electronic buffer to support opto-electronic-opto (o–e–o) conversion. The ports are therefore very expensive and thus their use must be limited. A router does not require any ports for a lightpath which optically bypasses the associated WXC switch. In our work, we consider fast dynamic routing of bandwidth-guaranteed sub-lambda label switched paths (LSPs) in GMPLS-capable integrated IP/WDM networks with limited number of ports. Our work aims to optimize the usage of resources such as bandwidth, wavelengths, and ports in order to route the LSPs with certain quality of service (QoS) requirements. The QoS requirements are specified in terms of the amount of bandwidth and maximum acceptable number of o–e–o conversions. We develop a graph model to represent the integrated network state. It models the port usage and the o–e–o conversion cost in addition to the cost of wavelength and bandwidth. We develop computationally simple path selection algorithms that optimize different cost metrics. We introduce the concept of differentiated QoS routing which provides service differentiation between high- and normal-priority LSPs with different QoS requirements. We then develop a threshold-protection-based routing algorithm which admits high-priority LSPs in preference to normal-priority LSPs. We demonstrate the effectiveness of our algorithms through extensive simulation results.