Analogous to multiple-symbol differential detection of quadrature phase-shift keying (QPSK), a multiple-bit differential detection scheme is described for offset QPSK that also exhibits continuous improvement in performance with an increasing observation interval. Being derived from maximum-likelihood (ML) considerations, the proposed scheme is purported to be the most power-efficient scheme for such a modulation and detection method. Extension of the results to shaped offset QPSK also is considered.