In the small-cell networks with multiple-input-single-output broadcasting (MISO-BC) backhauls, the joint dirty-paper coding and power control are investigated for the \mbox{MISO-BC} backhauls and access links in order to minimize the system transmit power. Considering the proportional rates of MISO-BC backhauls and flow-conservation constraints, the formulated optimization problem is \mbox{non-convex}. Moreover, the formulated problem couples the precoding vectors with the power-control variables. In order to handle the \mbox{non-convex} optimization problem and decouple the backhaul and access links, the structure of the formulated problem is investigated such that the optimal precoding vectors and optimal power-control variables are independently obtained. Moreover, the optimal precoding vectors are obtained in closed-form expressions. Simulation results are used to show the performance improvement over the benchmark scheme.