The UV-detectors of the CERES/NA45 experiment were originally conceived as parallel-plate counters with two-step amplification, an intermediate gate-electrode pair, and a final drift stage towards a pad electrode. Operated in beams of a few 10(6)/burst protons or S-32-nuclei at 200 GeV/u, this scheme was found to suffer from excessive spark rates, even in the gated mode. The origin of the sparks is quantitatively explained by event-correlated slow secondary particles, creating avalanches above the critical threshold of approximately 10(8) charges at the required gain of a few 10(5). This lack of sufficient dynamic range is also present in other schemes proposed in the literature; it severely limits the use of large-area parallel-plate counters for single-electron detection in a realistic high-energy physics environment. Possible improvements resulting from resistive anodes instead of metal meshes are also discussed. The spark problem of the CERES UV-detectors was solved by introducing wire amplification as the last stage. Laboratory tests showed a large increase in the dynamic range, due to a strong reduction (by factors of at least 20-30) of the net gain of the wire plane for high input charges via space-charge limitation. The residual spark rates of this scheme are lower by orders of magnitude and quite acceptable even for S-32-beams; gating was found to be unnecessary.