Pulsed-laser deposition was used to synthesize artificially layered high-temperature superconductors. Thin-film compounds were formed when the constraint of epitaxy was used to stabilize SrCuO2-BaCuO2 superlattices in the infinite layer structure. Using this approach, two new structural families, Ba2Srn-1Cun+1O2n+2+delta and Ba4Srn-1Cun+3O2n+6+delta, have been synthesized; these families superconduct at temperatures as high as 70 kelvin.