It is often the case in tomography that a scanner is unable to collect a full set of projection data. Reconstruction algorithms that are not set up to handle this type of problem can lead to artifacts in the reconstructed images because the assumptions regarding the size of the image space and/or data space are violated. In this study, we apply two recently developed geometry-independent methods to fully 3D multi-slice spiral CT image reconstruction. The methods build upon an existing statistical iterative reconstruction algorithm developed by our group. The first method reconstructs images without the missing data, and the second method seeks to jointly estimate the missing data and attenuation image. We extend the existing results for the 2D fan-beam geometry to multi-slice spiral CT in an effort to investigate some challenges in 3D, such as the long object problem. Unlike the original formulation of the reconstruction algorithms, a regularization term was added to the objective function in this work. To handle the large number of computations required by fully 3D reconstructions, we have developed an optimized parallel implementation of our iterative reconstruction algorithm. Using simulated and clinical datasets, we demonstrate the effectiveness of the missing data approaches in improving the quality of slices that have experienced truncation in either the transverse or longitudinal direction.