Hydrogen-poor planetary nebulae (PNe) Abell 58, Abell 78, and IRAS 15154-5258 were observed with the ISOPHOT low-resolution spectrometer on board the Infrared Space Observatory. Polycyclic aromatic hydrocarbon (PAH) features, commonly seen in H II regions, PNe, and in the diffuse interstellar medium, are absent from their infrared (IR) spectra. A 6.4 mu m dust feature is present instead in the IR spectra of Abell 78 and IRAS 15154-5258. We identify this feature as an aromatic C--C stretch feature produced in carbonaceous grains with little or no hydrogen. The 6.4 mu m feature is absent in the IR spectrum of the hydrogen-poor material in PN A58, which was ejected nearly 90 yr ago. Our observations of all three PNe are consistent with the hypothesis that the 6.4 mu m C--C stretch feature is produced by small, H-free carbonaceous grains, transiently heated to high temperatures by energetic stellar photons. The 6.4 mu m feature is not detected in A58 because of the presence of strong IR continuum produced by large, hot grains located close to its central star.