Heteronuclear spin decoupling in solid-state magic-angle spinning NMR is investigated to present methods overcoming interferences between rf irradiation and sample spinning in the intermediate to fast spinning regime. We demonstrate that a recent phase-alternated variant of refocused CW irradiation (rCW(ApA)) provides efficient and robust decoupling in this regime. An extensive experimental and numerical comparison is presented for rCW(ApA) and PISSARRO (phase-inverted supercycled sequence for attenuation of rotary resonance), previously introduced to quench rotary-resonance recoupling effects, under conditions with spinning frequencies between 30 and 60 kHz. Simulations are used to identify the effect of decoupling for various nuclear spin interactions. (C) 2015 Elsevier B.V. All rights reserved.