The asymmetry distributions for several kinematic variables are considered
for finding a systematic way to maximize the signal for the extraction
of the polarized gluon density. The relevance of mass effects for the
corresponding dijet cross section is discussed and the different approximations
for including mass effects are compared. We also compare via the
programs PEPSI and MEPJET two different Monte Carlo (MC) approaches for simulating the
expected signal in the dijet asymmetry at a polarized HERA.