The results of a new multi-channel deconvolution method applied to NORSAR and EKA array recordings of teleseismic P waves are presented and interpreted in terms of possible surface reflections and other arrivals from the Nevada Test Site and Kazakh nuclear explosions. The deconvolution method utilizes the well-known fact that P-wave spectra can be decomposed into source and receiver spectral factors. For most events, the source-time functions appear to contain a pP arrival but they also show later, unexplained arrivals. The site functions are also complex in many cases. About half of the late coda in P appears to be due to each source and receiver. The recordings for a presumed Kazakh cratering event show a distinctly different source function when compared to deeper, buried explosions at the same test site. From the deconvolved source-time functions, the cratering to noncratering mb bias is estimated to be between 0.09 and 0.22 magnitude units.