Ultraviolet and optical spectra are presented for three unusual Seyfert galaxies (Mrk 1239, Mrk 42, and Mrk 493) that resemble Seyfert 1 galaxies in that they have strong high-ionization lines and strong nonstellar continua, but resemble Seyfert 2 galaxies in that the widths of their permitted lines are as narrow as the widths of their forbidden lines. The He II lambda 1640 and He II lambda 4686 lines are used to determine an upper limit to the reddening experienced by the emission lines. Published optical data show that these particular high-ionization narrow-line (HINL) Seyferts have low [O III]lambda 5007/H-beta ratios and strong Fe II emission, which suggest the presence of high-density regions. The low L-alpha/H-beta ratios in these objects indicate that high-density clouds are indeed present, and, like the broad-line region clouds in Seyfert 1 galaxies, these clouds have large optical depths with partially ionized zones. Overall, the line ratios and continuum fluxes of these particular HINL Seyferts are indistinguishable from those of broad-lined Seyfert 1 galaxies.