We investigate theoretically intriguing aspects of a simple rotational-echo double-resonance (REDOR) NMR technique for homonuclear spin-1/2 pairs undergoingMAS. The simple technique sets Gaussian soft p pulses at every halfMAS rotational period in the pulse sequence. The reduction in rotational echo amplitude (the REDOR echo reduction) is observed at the end of the evolution period t(e) = (n+1) T-r, where T-r is aMAS rotational period. The exact average Hamiltonians for the homonuclear REDOR (hm-REDOR) technique are calculated by dividing the evolution period into four periods. We show theoretically and experimentally that the hm-REDOR technique produces the REDOR echo reductions for homonuclear spin-1/2 pairs. In addition, the theoretical results reveal that the REDOR echo reductions are independent of the chemical-shift difference, delta, under a simple condition of kappa = delta/omega(r)>= 6 and t(e)< 10 . (1/d'), where omega r is the sample spinning frequency and d' is the dipolar coupling constant expressed in Hz. We call this simple condition the master condition. This means that the REDOR echo reductions for a homonuclear spin-1/2 pair can be calculated under the master condition by considering only d' and omega(r), which is the case for a heteronuclear spin pair. Finally, we demonstrate that four-phase cycling yields the multiple-quantum filtered hm-REDOR experiment, where the appearance of the REDOR echo reductions shows that the echo reductions are definitely attributable to the homonuclear dipolar interaction even if there is a slight unwanted effect from the recovered chemical-shift anisotropy in these reductions. Copyright (C) 2015 JohnWiley & Sons, Ltd.