The adaptive moving grid strategy suggested in Part 1 for the solution of electrochemical kinetic problems in one-dimensional geometry has been examined thoroughly in calculations and developed further, with special emphasis laid on the resolution of extremely thin reaction layers at the electrodes. Numerical difficulties observed previously have been identified and eliminated. The use of a more accurate finite-difference approximation to second spatial derivatives in the regridding stage and padding of the monitor functions has led to a more reliable and nearly automatic spatial grid adaptation algorithm. Some improvement has also been achieved by using an expanding simulation layer. The improved algorithm has been applied to the example of linear potential scan voltammetric for the EC mechanism involving a fast homogeneous dimerization reaction.