PT ( = parity times time-reversal) symmetry of complex Hamiltonians with real spectra is usually interpreted as a weaker mathematical substitute for Hermiticity. Perhaps an equally important role is played by the related strengthened analyticity assumptions. In a constructive illustration we complexify a few potentials solvable only in s-wave. Then we continue their domain from the semi-axis to the whole axis and obtain new exactly solvable models. Their energies turn out to be real as expected. The new one-dimensional spectra themselves differ quite significantly from their s-wave predecessors.