We report on an investigation of the LANL method for determining the $O(a)$ improvement coefficient ${c}_{A}$ nonperturbatively. We find we are able to extract reliable estimates for the coefficient using this method. However, our study of systematic errors shows that for very accurate determinations of ${c}_{A},$ the smearing function must be tuned to keep the $O(a)$ ambiguity in ${c}_{A}$ fixed as $\ensuremath{\beta}$ varies. Consistency was found with previous results from the LANL group and (within fairly large errors) 1-loop perturbation theory; ${c}_{A}$ does not change significantly over the range $\ensuremath{\beta}=5.93--6.2.$ The big difference between our results and those of the ALPHA Collaboration, around $\ensuremath{\beta}=6.0,$ shows that the $O(a)$ differences in ${c}_{A}$ between the different methods can be large. We find that the lattice spacing dependence of ${f}_{\ensuremath{\pi}}$ and the renormalized quark mass is much smaller using our values of ${c}_{A}$ compared to those of the ALPHA Collaboration.