The authors present an iterative transmission reconstruction algorithm based on principles used for block-iterative emission reconstruction. Filtered backprojection (FBP) is adequate for transmission CT image reconstruction under ideal conditions. In cases where insufficient count rates are obtained, FBP suffers from significant biases. The authors' block-iterative transmission algorithm is developed by analogy to ordered-subset emission CT algorithms. They show similarities between their algorithm and a previously-proposed Ordered-Subset Convex (OSC) algorithm. Under ideal conditions, the authors' block-iterative transmission algorithm generates estimates of attenuation line integrals that are not significantly different from those from FBP or OSC. In the case of very low count-rate data, the authors' block-iterative algorithm produces line integral estimates that are less biased than those from FBP and nearly identical to those from OSC. They show that their algorithm is more computationally efficient than OSC, but that OSC performs slightly better with different subset configurations. It is concluded that both BIT and OSC are viable alternatives to FBP, especially under poor imaging conditions.