This paper studies the routing problems in Internet protocol/wavelength-division-multiplexing (IP/WDM) networks based on the overlay routing algorithm (ORA) and the integrated routing algorithm (IRA), respectively. Although IRA usually outperforms ORA in terms of blocking performance, IRA exhibits disadvantages in control information exchange, network privacy issue, and wavelength port efficiency. In this paper, a new mechanism called the short lightpath establishment approach (SLEA) is proposed for ORA in order to tackle the problems in IRA and achieve similar (or even better) network performance at the same time. The main idea of SLEA is to ensure that each new lightpath created by ORA is restricted by an optical hop constraint when a subwavelength-granularity connection is routed in the optical layer. It follows that SLEA essentially avoids per-connection-based greedy treatment and improves network wide resource utilization by eliminating inefficient long optical bypasses. To implement SLEA in ORA, the Dijsktra's algorithm has been modified based on an extended layered graph model. SLEA does not introduce any additional signaling and computational complexity. The analysis and simulation in this paper show that there exists an optimal optical hop constraint for each particular network configuration such that SLEA-based ORA (SLEA-ORA) can efficiently utilize the network resource of concern. As a result, with the optimal optical hop constraint, SLEA-ORA could outperform ORA and IRA in terms of the bandwidth-blocking ratio (BBR) and the average number of IP hops of label-switched paths (LSPs).