  In this paper we study classical general relativistic static wormhole
configurations with pseudo-spherical symmetry. We show that in addition to the
hyperbolic wormhole solutions discussed by Lobo and Mimoso in the Ref. Phys.\
Rev.\ D {\bf 82}, 044034 (2010), there exists another wormhole class, which is
truly pseudo-spherical counterpart of spherical Morris-Thorne wormhole
(contrary to the Lobo-Mimoso wormhole class), since all constraints originally
defined by Morris and Thorne for spherically symmetric wormholes are satisfied.
We show that, for both classes of hyperbolic wormholes the energy density, at
the throat, is always negative, while the radial pressure is positive, contrary
to the spherically symmetric Morris-Thorne wormhole. Specific hyperbolic
wormholes are constructed and discussed by imposing different conditions for
the radial and lateral pressures, or by considering restricted choices for the
redshift and the shape functions. In particular, we show that an hyperbolic
wormhole can not be sustained at the throat by phantom energy, and that there
are pseudo-spherically symmetric wormholes supported by matter with isotropic
pressure and characterized by space sections with an angle deficit (or excess).
