  We present two new NuSTAR observations of the narrow line Seyfert 1 (NLS1)
galaxy Mrk 766 and give constraints on the two scenarios previously proposed to
explain its spectrum and that of other NLS1s: relativistic reflection and
partial covering. The NuSTAR spectra show a strong hard (>15 keV) X-ray excess,
while simultaneous soft X-ray coverage of one of the observations provided by
XMM-Newton constrains the ionised absorption in the source. The pure reflection
model requires a black hole of high spin ($a>0.92$) viewed at a moderate
inclination ($i=46^{+1}_{-4}$ degrees). The pure partial covering model
requires extreme parameters: the cut-off of the primary continuum is very low
($22^{+7}_{-5}$ keV) in one observation and the intrinsic X-ray emission must
provide a large fraction (75%) of the bolometric luminosity. Allowing a hybrid
model with both partial covering and reflection provides more reasonable
absorption parameters and relaxes the constraints on reflection parameters. The
fractional variability reduces around the iron K band and at high energies
including the Compton hump, suggesting that the reflected emission is less
variable than the continuum.
