We conducted a Monte-Carlo study to investigate the influence of single-case research design chracteristics (phase length, initial DV level, intervention effect, trend) on the test power of piecewise Poisson-regression models. PLM have a high potential of adequately identifying intervention effects in single-case research designs. However, few measurement times, especially in phase A, and low initial DV levels make it impossible to detect even large intervention effects. Research designs with a high number of measurement times show robust power.