A new technique is presented for deconvolution of time series (digitally recorded temporal waveforms) such as obtained in acoustic emission. The method, called cross-cut deconvolution, combines two different least squares methods—one completely new, the other a recently developed variant of singular valued decomposition—to produce a potentially robust technique for treating ill-conditioned problems. A simple example is given for deconvolution of a Gaussian kernel in the presence of varying amounts of noise by each least squares method.