  Optimization of a positron crystal undulator (CU) is addressed. The ways to
assure both the maximum intensity and minimum spectral width of positron CU
radiation are outlined. We claim that the minimum CU spectrum width of 3 -- 4%
is reached at the positron energies of a few GeV and that the optimal bending
radius of crystals planes in CU ranges from 3 to 5 critical bending radii for
channeled particles. Following suggested approach a benchmark positron CU
construction is devised and its functioning is illustrated using the simulation
method widely tested by experimental data.
