The dominant X-ray emission of Seyfert galaxies has the form of a power law of mean photon index 1.9-2.0 which extends to at least 100 keV. However, recent observations, primarily from ROSAT, have revealed a subset of Seyfert galaxies with a qualitatively different X-ray appearance and unusual optical spectra. RE 1034+39, first identified in the ROSAT EUV survey, may be a prototype of this class of AGN. ROSAT and ASCA X-ray spectra are reported here, showing RE 1034+39 to have intense soft X-ray emission, together with an unusually steep 2-10 keV power law of photon index ~2.6, with possibly some contribution from ionized reflection. We speculate that an unusually high accretion rate is causing the intense soft X-ray flux, which - in turn - is Compton cooling the hard photon source, giving the observed steep spectrum at higher energies. The strong soft X-radiation may also be ionizing the disc and inhibiting the formation of the optical broad-line clouds. We point out the similarity of RE 1034+39 to the `high'-state spectra from the Galactic black hole candidate binary systems such as Cyg X-1.