The sensitivity of four tests on ShewhartQcharts and of specially designed EWMA and CUSUMQcharts to detect one-step permanent shifts of a Poisson parameter has been studied. The usual test that signals for one point beyond three standard deviations on a Shewhart chart is found to have poor sensitivity, generally. The test that signals when four out of five consecutive points are beyond one standard deviation in the same direction on a ShewhartQchart is found to be a good omnibus test. The EWMA and CUSUMQcharts are most sensitive to detect this particular type of instability and are about comparable in overall performance.