ScaLAPACK contains a pair of routines for solving systems which are narrow banded and diagonally dominant by rows. Mathematically, the algorithm is block cyclic reduction. The ScaLAPACK implementation can be improved using incomplete, rather than complete block cyclic reduction. If the matrix is strictly dominant by rows, then it is possible to bound the truncation error directly in terms of the dominance factor and the size of the partitions. Our analysis includes new results applicable in our ongoing work of developing an efficient parallel solver.