We consider in this letter the problem of constrained relay node (RN) placement where sensor nodes must be connected to base stations by using a minimum number of RNs. The latter can only be deployed at a set of predefined locations, and the two-tiered topology is considered where only RNs are responsible for traffic forwarding. We propose a one-step constrained RN placement (OSRP) algorithm which yields a network tree. The performance of OSRP in terms of the number of added RNs is investigated in a simulation study by varying the network density, the number of sensor nodes, and the number of candidate RN positions. The results show that OSRP outperforms the only algorithm in the literature for two-tiered constrained RNs placement.