It was a common practice from the 1950s to the 1970s for Asahi Optical Company to market their cameras in the United States through photographic equipment distributors who were well established in the U.S. market. Arrangements of this type began with the Asahiflex Ia, which was marketed as the Tower 23 (I.) by Sears Roebuck Company. The Asahiflex IIa was subsequently offered in the Sears Photographic Equipment Catalogs as the Tower 22, and the Asahiflex IIb was marketed as the Tower 23 (II.) with the 50mm lens and the Tower 24 with the 58mm lens. The distribution agreement with Sears was non-exclusive, and other distributors in the U.S. were simultaneously marketing the Asahiflex camera models. The Sears agreement concluded with the distribution of the original Asahi Pentax as the Tower 26, and the Asahi Pentax K as the Tower 29. Beginning with the production of the Pentax H2, Asahi Optical entered into an exclusive marketing agreement with Heiland Photographic of Denver, Colorado, the photographic equipment division of Minneapolis Honeywell Company.

Early in the production of the Heiland Pentax H2, Asahi manufactured a group of cameras which were specially labeled as "Store Demonstrator" models, apparently intended to be retained indefinitely by the camera shop to show off the features of the new product line. The "Store Demonstrator" lettering on these cameras was engraved into the front face of the top cover, directly ahead of the shutter button. Unlike the Heiland Pentax lettering on the prism front, which was done in a narrow arial style type, the "Store Demonstrator" lettering was a type style closer to Times New Roman. Both chrome and black cameras were lettered as "Store Demonstrator" models. On the chrome cameras, the lettering was not filled with black paint, and on the black cameras the lettering was not filled with white paint. This is the same as the way the "Honeywell" lettering on the prism top was treated on the Heiland Pentax cameras.

The "Store Demonstrator" H2 models observed by the writer fall in the serial number group from 210,000 to about 222,000. However, based on the infrequency of finding these cameras, I seriously doubt that much of the group of serial numbers in between was lettered as "Store Demonstrator" models. Probably several successive orders were produced at various times.
Based on a number of years of observation of camera shows and the eBay internet auction, the "Store Demonstrator" H2 cameras turn up about 1/3 as often as the Pentax "S" camera (3000+ produced), so a realistic estimate would probably be that around 1000 of these cameras may have been issued. The black version of the camera is extremely uncommon.