  We present a re-analysis of the XMM-Newton and NuSTAR observing campaign for
the well-studied, X-ray-bright AGN MCG-06-30-15. In particular, we consider a
disc model with finite thickness. By fitting the disc reflection spectra in the
data, we obtain a black hole spin of 0.87--0.99 (90\% confidence range) after
taking the thickness of the disc into consideration. Spectral models with a
grid of mass accretion rate from 0 to $30\%\dot{M}_{\rm Edd}$ are calculated
for MCG-06-30-15. This result is obtained by considering a free disc reflection
fraction parameter $f_{\rm refl}$ and is consistent with previous measurements
based on razor-thin disc models. Besides, an isotropic, point-like geometry,
i.e. the `lamppost' geometry, is assumed for the corona in our model. We find
that such a geometry overestimates $f_{\rm refl}$ in the data. Therefore, thin
disc models with consistent `lamppost' values of $f_{\rm refl}$ provide a worse
fit than ones with a free $f_{\rm refl}$ parameter. We discuss possible reasons
for the discrepancy between the observed and theoretical values of $f_{\rm
refl}$ at the end of the paper. Modifications for the over-simplified lamppost
model might be needed when the thickness of the thin disc is considered in
future work.
