Preliminary results of a sensitive search for low-luminosity Seyfert 1 nuclei are presented. The sample contained a total of 75 galaxies with spectral resolutions of 2.5 A, and high signal-to-noise ratios of about 100/1 in the range 6200-6880 A. The search was carried out using the Palomar Hale telescope and a double spectrograph. The wavelengh scale was established by fitting a quartic polynomial to unblended emission lines from the Ar and Ne comparison spectra. In comparison with forbidden emission, H-alpha emission exhibited broad wings in 19-28 objects, including 3-5 E or E/50 galaxies. Op the twenty Liner galaxies in the sample, 8-12 showed broad H-alpha lines with smaller equivalent widths than in low-luminosity AGNs. The forbidden line of O I in one third of the Liner galaxies was broader than the S II forbidden line. On the basis of the preliminary results, it is suggested that that the faint end of the luminosity function of AGNs is more populated than has previously been believed. A list of the observations is given.