Composite spin-state-selective rotations are introduced. They are devised to remedy the following problem: When determining scalar plus residual dipolar couplings by conventional NMR experiments in partially aligned molecules, a considerable variation in the effective coupling constant often entails systematic errors compromising the accuracy of the measurements. The concept of composite pulses is extended in order to design spin-state-selective composite rotations ((SCR)-C-3) robust to variation in effective coupling constants. With the (SCR)-C-3 approach the broadband performance of spin-state-selective excitation improves significantly as is demonstrated both numerically and experimentally.