The primary step in tissue cytometry is the automated distinction of individual cells (segmentation). Since cell borders are seldom labeled, cells are generally segmented by their nuclei. While tools have been developed for segmenting nuclei in two dimensions, segmentation of nuclei in three-dimensional volumes remains a challenging task. The lack of effective methods for three-dimensional segmentation represents a bottleneck in the realization of the potential of tissue cytometry, particularly as methods of tissue clearing present the opportunity to characterize entire organs. Methods based on deep learning have shown enormous promise, but their implementation is hampered by the need for large amounts of manually annotated training data. In this paper, we describe 3D Nuclei Instance Segmentation Network (NISNet3D) that directly segments 3D volumes through the use of a modified 3D U-Net, 3D marker-controlled watershed transform, and a nuclei instance segmentation system for separating touching nuclei. NISNet3D is unique in that it provides accurate segmentation of even challenging image volumes using a network trained on large amounts of synthetic nuclei derived from relatively few annotated volumes, or on synthetic data obtained without annotated volumes. We present a quantitative comparison of results obtained from NISNet3D with results obtained from a variety of existing nuclei segmentation techniques. We also examine the performance of the methods when no ground truth is available and only synthetic volumes were used for training.