  Extending previous studies of nonthermal electron transport in solar flares
which include the effects of collisional energy diffusion and thermalization of
fast electrons, we present an analytic method to infer more accurate estimates
of the accelerated electron spectrum in solar flares from observations of the
hard X-ray spectrum. Unlike for the standard cold-target model, the spatial
characteristics of the flaring region, especially the necessity to consider a
finite volume of hot plasma in the source, need to be taken into account in
order to correctly obtain the injected electron spectrum from the
source-integrated electron flux spectrum (a quantity straightforwardly obtained
from hard X-ray observations). We show that the effect of electron
thermalization can be significant enough to nullify the need to introduce an
{\it ad hoc} low-energy cutoff to the injected electron spectrum in order to
keep the injected power in non-thermal electrons at a reasonable value. Rather
the suppression of the inferred low-energy end of the injected spectrum
compared to that deduced from a cold-target analysis allows the inference from
hard X-ray observations of a more realistic energy in injected non-thermal
electrons in solar flares.
