  Using {\em RHESSI} hard X-ray imaging spectroscopy observations, we analyze
electron flux maps for a number of extended coronal loop flares. For each
event, we fit a collisional model with an extended acceleration region to the
observed variation of loop length with electron energy $E$, resulting in
estimates of the plasma density in, and longitudinal extent of, the
acceleration region. These quantities in turn allow inference of the number of
particles within the acceleration region and hence the filling factor $f$ --
the ratio of the emitting volume to the volume that encompasses the emitting
region(s). We obtain values of $f$ that lie mostly between 0.1 and 1.0; the
(geometric) mean value is $f = 0.20 \times \div 3.9$, somewhat less than, but
nevertheless consistent with, unity. Further, coupling information on the
number of particles in the acceleration region with information on the total
rate of acceleration of particles above a certain reference energy (obtained
from spatially-integrated hard X-ray data) also allows inference of the
specific acceleration rate (electron s$^{-1}$ per ambient electron above the
chosen reference energy). We obtain a (geometric) mean value of the specific
acceleration rate $\eta(20$ keV) $ = (6.0 \times / \div 3.4) \times 10^{-3}$
electrons s$^{-1}$ per ambient electron; this value has implications both for
the global electrodynamics associated with replenishment of the acceleration
region and for the nature of the particle acceleration process.
