An important approach to reconstructing PET and SPECT (PET/SPECT) radiotracer images is to utilize high-resolution information from registered MRI or CT (MRI/CT) images. These methods depend on accurate registration of PET/SPECT and MRI/CT images. Herein, we consider registration via optimization of a PET/SPECT image-reconstruction objective function which includes the registration parameters. Potential benefits of this approach include 1) modeling, within the registration process, of PET/SPECT noise and PET/SPECT acquisition effects such as limited spatial resolution, perhaps resulting in more accurate registration and 2) a natural framework for calculating joint uncertainties in registration parameters and radiotracer activity. In cases where the structures imaged by MRI/CT (e.g., gray matter and white matter in the brain) strongly influence the radiotracer distribution, the relatively small number of variables comprised of alignment parameters and regional radiotracer mean activities may account for, not all, but much of the estimable radiotracer distribution, and it may be useful to develop methods for rapid, highly accurate estimation of these few parameters, ultimately embedding such estimation within more general estimation of the full radiotracer distribution. Herein we develop Levenberg-Marquardt simultaneous estimation of regional radiotracer mean activities and the six 3D rigid body translation and rotation alignment parameters. The method is tested by a computer-simulation study. With a PET/SPECT scanner spatial resolution of 0.2 cm FWHM, this study shows translational registration errors of about 0.002 cm and rotational errors which are fractions of a degree. For small regions, estimates of regional mean activities are much closer to true values than are estimates obtained by OSEM using PET/SPECT projection data only.