  We study the evolution of the spectral index and the normalization (flux) of
the non-thermal component of the electron spectra observed by RHESSI during 24
solar hard X-ray flares. The quantitative evolution is confronted with the
predictions of simple electron acceleration models featuring the soft-hard-soft
behaviour. The comparison is general in scope and can be applied to different
acceleration models, provided that they make predictions for the behavior of
the spectral index as a function of the normalization. A simple stochastic
acceleration model yields plausible best-fit model parameters for about 77% of
the 141 events consisting of rise and decay phases of individual hard X-ray
peaks. However, it implies unphysically high electron acceleration rates and
total energies for the others. Other simple acceleration models such as
constant rate of accelerated electrons or constant input power have a similar
failure rate. The peaks inconsistent with the simple acceleration models have
smaller variations in the spectral index. The cases compatible with a simple
stochastic model require typically a few times 10^36 electrons accelerated per
second at a threshold energy of 18 keV in the rise phases and 24 keV in the
decay phases of the flare peaks.
