Three-dimensional statistical iterative reconstruction (SIR) algorithms have the potential to significantly reduce image artifacts by minimizing a cost function that models the physics and statistics of the data acquisition process in x-ray CT. SIR algorithms are important for a wide range of applications including nonstandard geometries arising from irregular sampling, limited angular range, missing data, and low-dose CT. For iterative image reconstruction algorithms to be deployed in clinical settings, the images must be quantitatively accurate and computed in clinically useful times. We describe an acceleration method that is based on adaptively varying an update factor of the additive step of the alternating minimization (AM) algorithm. Our implementation combines this method with other acceleration techniques like ordered subsets (OS) which was originally proposed for transmission tomography by Ahn, Fessler et. al [1]. Results on both an NCAT phantom and real clinical data from a Siemens Sensation 16 scanner demonstrate an improved convergence rate compared to the straightforward implementations of the alternating minimization (AM) algorithm of O'Sullivan and Benac [2] with a Huber-type edge-preserving penalty, originally proposed by Lange [3]. Our proposed acceleration method on average yields 2X acceleration of the convergence rate for both baseline and ordered subset implementations of the AM algorithm.