A novel strategy for heteronuclear dipolar decoupling in magic-angle spinning solid-state NMR spectroscopy is presented, which eliminates residual static high-order terms in the effective Hamiltonian originating from interactions between oscillating dipolar and anisotropic shielding tensors. The method, called refocused continuous-wave (rCW) decoupling, is systematically established by interleaving continuous wave (CW) decoupling with appropriately inserted rotor-synchronized high-power π refocusing pulses of alternating phases. The effect of the refocusing pulses in eliminating residual effects from dipolar coupling in heteronuclear spin systems is rationalized by effective Hamiltonian calculations to third order. In some variants the π pulse refocusing is supplemented by insertion of rotor-synchronized π/2 purging pulses to further reduce the residual dipolar coupling effects. Five different rCW decoupling sequences are presented and their performance is compared to state-of-the-art decoupling methods. The rCW decoupling sequences benefit from extreme broadbandedness, tolerance towards rf inhomogeneity, and improved potential for decoupling at relatively low average rf field strengths. In numerical simulations, the rCW schemes clearly reveal superior characteristics relative to the best decoupling schemes presented so far, which we to some extent also are capable of demonstrating experimentally. A major advantage of the rCW decoupling methods is that they are easy to setup and optimize experimentally.