  We present high-quality spectra of the majority of stars that have been
classified as Oe and find that their published spectral types are generally too
early, most likely due to infilling of HeI lines. As a matter of fact, all
stars classified as Oe actually fall inside the range O9-B0 with the important
exception of HD155806 (O7.5III) and perhaps HD39680 (difficult to classify, but
likely O8.5V). Observations of a sample of objects with published spectral
types in the O9-B0 range previously classified as peculiar or emission-line
stars fail to reveal any new Oe star with spectral type earlier than O9.5. Most
objects classified as peculiar in ``classical'' literature show signs of
binarity in our spectra, but no spectral anomalies. We conclude that there is
likely a real decline in the fraction of Be stars for spectral types earlier
than B0, not due to observational bias. The few Oe stars with spectral types
earlier than O9.5 deserve detailed investigation in order to provide
constraints on the physical reasons of the Be phenomenon.
