  The properties of underluminous type Ia supernovae (SNe Ia) of the 91bg
subclass have yet to be theoretically understood. Here, we take a closer look
at the structure of the dim SN Ia 2005bl. We infer the abundance and density
profiles needed to reproduce the observed spectral evolution between -6 d and
+12.9 d with respect to B maximum. Initially, we assume the density structure
of the standard explosion model W7; then we test whether better fits to the
observed spectra can be obtained using modified density profiles with different
total masses and kinetic energies. Compared to normal SNe Ia, we find a lack of
burning products especially in the rapidly-expanding outer layers (v>~15000
km/s). The zone between ~8500 and 15000 km/s is dominated by oxygen and
includes some amount of intermediate mass elements. At lower velocities,
intermediate mass elements dominate. This holds down to the lowest zones
investigated in this work. This fact, together with negligible-to-moderate
abundances of Fe-group elements, indicates large-scale incomplete Si burning or
explosive O burning, possibly in a detonation at low densities. Consistently
with the reduced nucleosynthesis, we find hints of a kinetic energy lower than
that of a canonical SN Ia: The spectra strongly favour reduced densities at
>~13000 km/s compared to W7, and are very well fitted using a rescaled W7 model
with original mass (1.38 M_sun), but a kinetic energy reduced by ~30 % (i.e.
from 1.33e51 erg to 0.93e51 erg).
