We present a special case of the theory of coherent isotropic averaging in zero-field NMR, given in part I of this work. In a zero external field, combinations of the magnetic-field pulses restricted to pi/2 rotations along the three coordinate axes can selectively average internal spin Hamiltonians while preserving the intrinsic invariance of the spectrum with respect to the sample orientation. Compared with the general case, the limits of the allowed scaling factors of first- and second-rank interactions are slightly reduced. For instance, time reversal is possible for second-rank tensors with a -1/5 scaling factor, instead of -1/4 in general. Finite pulse compensations are analyzed and experimental illustrations are given for two optimum time-reversal sequences. The cubic sequences, though less efficient than the icosahedral sequences, are technically more feasible and may be used in zero-field experiments such as decoupling (by rank or nuclear species), time reversal or multipolar experiments (the zero-field equivalent of multiple-quantum NMR).