  The characteristic anti-linear (parity/time reversal, PT) symmetry of
non-Hermitian Hamiltonians with real energies is presented as a source of two
new forms of solvability of Schr\"{o}dinger's bound-state problems. In detail
we describe (1) their very specific semi-exact solvability (SES) and (2) their
innovated variational tractability. SES technicalities are discussed via
charged oscillator example. In a broader context, speculations are added
concerning possible relationship between PT symmetry, solvability and
superintegrability.
