We have defined a sample of 63 AGN with strong forbidden high-ionisation line (FHIL) emission. These lines, with ionisation potentials >~ 100eV, respond to a portion of the spectrum that is often difficult to observe directly, thereby providing constraints on the EUV-soft X-ray continuum. The sources are selected from the Sloan Digital Sky Survey (SDSS) on the basis of their [Fe X]6374A emission, yielding one of the largest and the most homogeneous sample of FHIL-emitting galaxies. We fit a sequence of models to both FHILs ([Fe XI], [Fe X] and [Fe VII]) and lower-ionisation emission lines ([O III], [O I], H-alpha, [N II], [S II]) in the SDSS spectra. These data are combined with X-ray measurements from Rosat, which are available for half of the sample. The correlations between these parameters are discussed for both the overall sample and subsets defined by spectroscopic classifications. The primary results are evidence that: (1) the [Fe X] and [Fe XI] lines are photoionised and their strength is proportional to the continuum flux around 250 eV; (2) the FHIL-emitting clouds form a stratified outflow in which the [Fe X] and [Fe XI] source regions extend sufficiently close to the BLR that they are partially obscured in Seyfert 2s whereas the [Fe VII] source region is more extended and is unaffected by obscuration; (3) narrow-lined Seyfert 1s (NLS1s) tend to have the strongest [Fe X] flux (relative to lower-ionisation lines); and (4) the most extreme [Fe X] ratios (such as [Fe X]/[O III] or [Fe X]/[Fe VII]) are found in the NLS1s with the narrowest broad lines and appear to be an optical-band indication of objects with strong X-ray soft excesses.
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