This short paper studies convergence properties, particularly asymptotic convergence, of the block-iterative Fisher scoring (BFS) algorithms recently proposed by Ma and Hudson (2008). While applicable in other inverse problem domains (e.g. astronomy, geophysics, signal processing or remote sensing), this class of algorithms was designed for tomographic image reconstruction from projections in medicine. A BFS algorithm is used to reconstruct the patient's internal structural or functional activity from collected projection data. We briefly introduce the BFS algorithm and a general convergence result provided in Ma and Hudson (2008). This result is used to prove the asymptotic convergence of two specific BFS algorithms under new conditions.