Perovskite titanates with nominal stoichiometry ABO(3+delta) often exhibit quite interesting properties, but their structural characterization is not always rigorous. Herein, we demonstrate how excess oxygen can be incorporated in a titanate perovskite based lattice. A new family of layered perovskites La4Srn-4TinO3n+2 has been investigated by means of X-ray diffraction neutron diffraction transmission electron microscopy, thermogravimetric analysis, and density and magnetic measurements. Such layered perovskites are known to be able to accommodate extra oxygen beyond the parental ABO(3) perovskite in crystallo-graphic shears. The structure evolves with increasing n. Firstly, the perovskite blocks become more extensive an the oxygen intergrowth layers move further apart; then the spacing between the intergrowth layers increases further and their repetition becomes more sporadic. Finally the layered structure is lost for the n = 12 member (La2Sr4Ti6O19-delta). In this structure, excess oxygen is accommodated within the perovskite framework in randomly distributed short-range linear defects. These defects become more dilute as the cubic perovskite, that is, n = infinity, composition is approached.