  Determining the properties of starbursts requires spectral diagnostics of
their ultraviolet radiation fields, to test whether very massive stars are
present. We test several such diagnostics, using new models of line ratio
behavior combining Cloudy, Starburst99 and up-to-date spectral atlases. For six
galaxies we obtain new measurements of HeI 1.7 um / Brackett 10, a difficult to
measure but physically simple (and therefore reliable) diagnostic. We obtain
new measurements of HeI 2.06 um / Brackett gamma in five galaxies, and find
that it and [OIII]/Hbeta are generally unreliable diagnostics in starbursts.
The heteronuclear and homonuclear mid--infrared line ratios (notably [NeIII]
15.6 um / [NeII] 12.8 um) consistently agree with each other and with HeI 1.7
um / Br10; this argues that the mid-infrared line ratios are reliable
diagnostics of spectral hardness. In a sample of 27 starbursts, [NeIII]/[NeII]
ratios are significantly less excited than model predictions for a Salpeter IMF
extending to 100 solar masses. Plausible model alterations strengthen this
conclusion. By contrast, the low-mass and low-metallicity galaxies II Zw 40 and
NGC 5253 show relatively high neon line ratios, compatible with a Salpeter
slope extending to at least 40--60 Msol. One solution for the low neon line
ratios in the high--metallicity starbursts would be that they are deficient in
>40 Msol stars compared to a Salpeter IMF. An alternative explanation, which we
prefer, is that massive stars in high--metallicity starbursts spend much of
their lives embedded within ultra--compact HII regions that prevent the near-
and mid-infrared nebular lines from forming and escaping. This hypothesis has
important consequences for starburst modelling and interpretation.
