We present comparisons of broad H alpha and H beta profiles of a low-redshift, high-signal-to-noise sample of AGNs with highly asymmetric Balmer line profiles. We have removed contamination by narrow emission lines, host galaxy starlight, and broad Fe II emission. We fit the AGN continuum with a reddened standard, externally-illuminated accretion disk. We demonstrate how the cleaned, highly-asymmetric Balmer line profiles can be readily fit simply by partial obscuration of a tilted standard broad-line region. The difference between AGNs with only slightly asymmetric Balmer line profiles and our sample of extremely asymmetric profiles is consistent with the latter sample having a large area of the broad-line region obscured.