  The collisional thick target model (CTTM) of solar hard X-ray (HXR) bursts
has become an almost 'Standard Model' of flare impulsive phase energy transport
and radiation. However, it faces various problems in the light of recent data,
particularly the high electron beam density and anisotropy it involves.} {We
consider how photon yield per electron can be increased, and hence fast
electron beam intensity requirements reduced, by local re-acceleration of fast
electrons throughout the HXR source itself, after injection.} {We show
parametrically that, if net re-acceleration rates due to e.g. waves or local
current sheet electric (${\cal E}$) fields are a significant fraction of
collisional loss rates, electron lifetimes, and hence the net radiative HXR
output per electron can be substantially increased over the CTTM values. In
this local re-acceleration thick target model (LRTTM) fast electron number
requirements and anisotropy are thus reduced. One specific possible scenario
involving such re-acceleration is discussed, viz, a current sheet cascade (CSC)
in a randomly stressed magnetic loop.} {Combined MHD and test particle
simulations show that local ${\cal E}$ fields in CSCs can efficiently
accelerate electrons in the corona and and re-accelerate them after injection
into the chromosphere. In this HXR source scenario, rapid synchronisation and
variability of impulsive footpoint emissions can still occur since primary
electron acceleration is in the high Alfv\'{e}n speed corona with fast
re-acceleration in chromospheric CSCs. It is also consistent with the
energy-dependent time-of-flight delays in HXR features.
