In a first attempt I fed the H-pole in the center with a ladder line. It was electrically no longer an "off-center-fed-dipole" as the C-Pole was, but a vertical, folded "doublet".
The C-Pole is a resonant antenna, whereas the H-Pole is non resonant and must be matched with a tuner.
Construction and materials used for the H-Pole are similar to the C-Pole.
The first results are very promising. I had contacts with excellent signal reports within a few minutes on all bands except 80m at @ 12:00 UTC in July 2008.
I used the SG-239 Automatic Tuner (asymmetric !). So far, the sound of the automatic tuner, was "healthy", only a few "clicks" and down was the SWR! I connected the lower half of the H-Pole to the ground connector, the upper half to the "hot" side of the tuner output.


Elevation Diagrams H-Pole [black] Versus C-Pole [blue], 0.5m over MININEC-Ground, 20m-Band
The Azimut Diagrams for both antennas are omnidirectional

Elevation Diagrams H-Pole 3.7MHz [blue], 7.06MHz [green], 14.24MHz [black], 21.24MHz [violett], 28.5MHz [light blue],
0.5m over MININEC-Ground
See EZNEC-File: multi-h-pole-tl.ez
Only after Peter (HB9CET) asked: "Why don't you feed at the bottom?" I checked for the best feedpoint around the lower part of the antenna and found an optimum, both electrically and mechanically: the lower horizontal wire (#6 in the EZNEC-File).


Elevation Diagrams off-center fed H-Pole [black] versus center fed H-Pole [blue]
20m Band, 0.5m over MININEC-Ground

Azimut Diagrams off-center fed H-Pole [black] versus center fed H-Pole [blue]
20m Band, 0.5m over MININEC-Ground
See EZNEC-File: multi-h-polecet.ez