The effects of partial substitution of Ba for Sr on the superconducting transition in the sulphate containing materials [Y0.74Ca0.16Sr0.1]Sr2Cu2.78(SO4)0.22O6.12 and [Y0.84Sr0.16]Sr2Cu2,78(SO4)0.22O6.12 have been investigated. As the Ba content was increased, the superconducting transitions became sharper and Tc onset increased to reach a maximum of 78 K. The cell symmetry was also observed to change from orthorhombic to tetragonal, which is thought to be associated with randomization of the orientations of the sulphate groups in the structure.