Morey's chief contribution to the phonautograph seems to have been a particular kind of lever arm which offered less resistance to movement and hence produced better curves than previous models.
Bell in particular mentions Morey's improvements and uses them to springboard off on his own path.
Knight's American Mechanical Dictionary, in "Telephone", p.2514. (1880: Riverside Press, Cambridge) takes the following from "American Journal of Science and Arts," August, 1874, pages 130, 131:
Fig. 6257 shows curves obtained by Mr. Charles A. Morey by the interposition of a light lever between the membrane and the smoked glass, which is drawn along beneath the style, whose excursions are much magnified by the lever. . . .
See also phonautograph.