In fluorescence lifetime imaging microscopy (FLIM), fluorescence time decay at each pixel of the imaged sample are measured. Every recorded fluorescence decay corresponds to the time convolution of the instrument response with the intrinsic fluorescence impulse response function (IRF), from which the sample fluorescence lifetime is determined. To estimate the IRF, the instrument response thus needs to be deconvolved from the recorded fluorescence decay. We have recently introduced a novel FLIM time-deconvolution method based on the linear expansion of the fluorescence decays on an orthonormal Laguerre basis. Since this method allows simultaneous estimation of the IRFs at all pixels, it performs at least two orders of magnitude faster than standard algorithms. In its original implementation, however, the Laguerre basis, determined by the Laguerre parameter , is selected using a heuristic approach. Here, we present an automated implementation, whereby the Laguerre parameter is treated as a free parameter within a nonlinear least squares optimization scheme. The new implementation combines the unmatched inherent computational speed of the Laguerre deconvolution method with a systematic model selection approach. This method will thus facilitate applications of FLIM requiring automatic estimation of the spatial distribution of fluorescence lifetimes, such as in in vivo tissue FLIM imaging.