Satellite transition rotational resonance and magic-angle effects on central-transition spin-echo decay and inversion recovery of half-integer quadrupolar nuclei are presented. Small magic-angle offsets can change the satellite transition rotational resonance condition and consequently lead to dramatic effects on line width, spin-echo decay and inversion recovery. An half degree magic-angle offset lengthens α-Al2O3 spin-echo decay by 50% and inversion-recovery by nearly two orders of magnitude. The theory of satellite transition rotational resonance is presented and the origin of these magic-angle effects is explained.