  We design, from first principles calculations, a novel family of thallium
halide-based compounds as candidates for new high temperature superconductors,
whose superconductivity is mediated by the recently proposed mechanism of
non-local correlation-enhanced strong electron-phonon coupling. Two prototype
compounds namely CsTlF$_3$ and CsTlCl$_3$ are studied with various hole doping
levels and volumes. The critical superconducting temperature T$_c$ are
predicted to be about 30 K and 20 K with $\sim$0.35/f.u. hole doping and
require only modest pressures ($\sim$10 and $\sim$2 GPa), respectively. Our
procedure of designing this class of superconductors is quite general and can
be used to search for other "other high temperature superconductors".
