We have used the ROSAT Bright Source Catalogue to extract a complete sample of sources selected in the band from 0.1-0.4 keV. This 0.25 keV-selected sample is composed of 54 Seyfert galaxies, 25 BL Lacertae objects, 4 clusters and 27 Galactic stars or binaries. Seyfert-type galaxies with 'ultrasoft' X-ray spectra can very often be classed optically as narrow-line Seyfert 1s (NLS1s). Such objects are readily detected in 0.25 keV surveys; the sample reported here contains 20 NLS1s, corresponding to a 40 per cent fraction of the Seyferts. Optical spectra of the Seyfert galaxies were gathered for correlative analysis, which confirmed the well-known relations between X-ray slope and optical spectral properties (e.g. [QIII]/Hβ ratio; Fe II strength, Hβ width). The various intercorrelations are most likely driven, fundamentally, by the shape of the photoionizing continuum in Seyfert nuclei. We argue that a steep X-ray spectrum is a better indicator of an 'extreme' set of physical properties in Seyfert galaxies than is the narrowness of the optical Hβ line. The correlation studies were also used to isolate a number of Seyfert galaxies with apparently 'anomalous' properties. Of particular interest are the six objects with relatively weak permitted line emission (Hβ and Fe II) and weak optical continua. Such objects are rare in most surveys, but two of these (IC 3599 and NGC 5905) are known to be transient active galactic nuclei in which the X-ray flux has faded by factors ∼100. If the other four objects also turn out to be transient, this would demonstrate that 0.25 keV surveys provide an efficient way of finding an interesting class of object. Finally, the luminosity function of the 0.25 keV-selected Seyfert galaxies was determined and broken down into subsamples to investigate the relative space densities of Seyferts when separated on the basis of either X-ray slope or Hβ linewidth.