The nuclei 143,145,147Ba produced in the spontaneous fission of 248Cm have been studied using the EUROGAM phase II array. The parities and multipolarities of γ rays in these nuclei have been assigned from triple angular correlation, directional linear-polarisation correlation and internal conversion coefficient measurements. These data confirm an alternating-parity sequence connected by strong electric dipole transitions in 143Ba. They also reveal a more weakly populated, complementary alternating-parity sequence. The two sequences together exhibit some characteristics of parity-doublet bands. Interpreting the E1 strengths in terms of a rotating intrinsic dipole moment gives a moment similar in size to that observed in 142Ba and 144Ba. No well-developed similar structure is seen in 145Ba, although E1 transitions are observed, from which a value of the dipole moment is obtained. This value is smaller than the moment observed in 143Ba. No features appropriate to strong octupole correlations were observed in 147Ba.