The blind deconvolution algorithm for 3D transmitted light brightfield (TLB) microscopy, published previously [Holmes et al. Handbook of Biological Confocal Microscopy (1995)], is summarized with example images. The main emphasis of this paper is to discuss more thoroughly the importance and usefulness of this method and to provide more detailed evidence, some being quantitative, of its necessity. Samples of horseradish peroxidase (HRP)-stained pyramidal neurones were prepared and evaluated for the ability to see fine structures clearly, including the dendrites and spines. It is demonstrated that the appearance of fine spine structure, and means of identifying spine categories, is made possible by using blind deconvolution. A comparison of images of the same sample from reflected light confocal microscopy, which is the conventional light microscopic way of viewing the 3D structure of these HRP-stained samples, shows that the blind deconvolution method is far superior for clearly showing the structure with less distortion and better resolution of the spines. The main significance of this research is that it is now possible to obtain clear images of 3D structure by light microscopy of absorbing stains. This is important because the TLB microscope is probably the most widely used modality in the life-science laboratory, yet, until now, there has been no reliable means for it to provide visualization of 3D structure clearly. The main importance of the blind deconvolution approach is that it obviates the need to measure the point spread function of the optical system, so that it now becomes realistic to provide a 3D light microscopic deconvolution method that can be pervasively used by microscopists.