This paper describes the finding of an experimental study to measure the detector paralysis factor and the use of this parameter in conjunction with detector dead time to better model detector dead-time response. The idealized one-parameter models, the paralyzable and nonparalyzable models, are inadequate to properly model the dead-time response of any real detector system. To address this deficiency, a more realistic two-parameter model is proposed that incorporates the paralysis factor of the detector in addition to the dead time. The revised two-parameter-based model is an extension of Lee and Gardner's two-dead-time model. A simple scheme is proposed to deduce these parameters from the recorded data based on the rise and drop of count rates from a decaying source. Measurements were made using 56Mn and 52V. The data collected in this study show that a high-purity germanium (HPGe) detector has a paralysis factor of ~50 to 77% and a dead time of 6 to 10 s. Using the data collected by Lee and Gardner, the paralysis factor for a Geiger-Mueller (GM) counter is estimated to be ~5%. These results are consistent with the approximating assumption that GM counters are nonparalyzing and HPGe detectors are paralyzing.