Seismic data recorded at the broad-band teleseismic GRF array and theshort-period regional GERESS array, which is a designated IMS primarystation, are analyzed to determine the effectiveness of teleseismic P-wave complexity for the purpose of seismic event screening within theframework of Comprehensive Nuclear-Test-Ban Treaty verification. For theGRF array, seismic waveform data from nearly 200 nuclear explosions havebeen recorded since its installation in the late 1970's, which were studiedalong with several thousand earthquakes from the last few years.Additionally, we investigated teleseismic P wave complexity for a similarnumber of earthquakes recorded at GERESS. However, owing to itsoperation starting in 1991, only a limited number of nuclear explosionseismograms are available for study.For nuclear explosions, complexity does not exceed levels of 0.3 except fora number of events from the Nevada Test Site recorded only at the GRFarray and located at a large distance where PcP may interfere with the initialP wavelet. Since all events with complexity at GRF larger than 0.3 areexclusively located on Pahute Mesa within the Nevada Test Site,near-source geology or topography must play a dominant role for theseincreased complexity values, while PcP may not contribute significantly tothe high-frequency energy measured by the complexity parameter.Although many earthquakes show complexities below this level, for morethan 25% of the earthquakes investigated the complexities determined arelarger than 0.7, thus showing distinctly larger values than nuclearexplosions. Therefore, this percentage may be screened as earthquakes fromall seismic events detected. As currently only about half of the eventsdetected by the global IMS network are screened out based on focal depthand the mb:Ms criterion, teleseismic P-wavecomplexity may contribute significantly to the task of seismic eventscreening.