A bore finishing process, comprising steps of: determining an initial value for at least one parameter of a bore to be finished, and a final value for the at least one parameter of the bore; then automatically determining a set of process parameters for controlling at least one bore finishing iteration wherein a finishing tool will be rotated and reciprocated within the bore for removing material from the surface defining the bore to change the at least one parameter of the bore so as to have an in-process value equal to the final value or that has progressed from the initial value toward the final value; and performing the bore finishing iteration under control of the process parameters and measuring the in-process value at known axial locations in the bore; wherein the measured in-process values are automatically mathematically treated to determine an optimized set of values for the process parameters for a next bore finishing iteration for achieving a target value for the at least one parameter of the bore of the next iteration within specified limits characterized - in that the optimized set of values for the process parameters for a next bore finishing iteration includes at least one parameter of a stroke of the reciprocation and a duration of the next iteration, and - in that the set of process parameters comprises at least one parameter of the finishing tool configured as a function of at least one predictive factor for changing the at least one parameter of the bore by a predetermined amount, and - by a step of automatically determining whether the at least one parameter of the bore changed during the iteration by at least the predetermined amount; and i. if yes, then continuing to use the at least one predictive factor; and ii. if no, then changing the at least one predictive factor for a subsequent iteration. determining an initial value for at least one parameter of a bore to be finished, and a final value for the at least one parameter of the bore; then automatically determining a set of process parameters for controlling at least one bore finishing iteration wherein a finishing tool will be rotated and reciprocated within the bore for removing material from the surface defining the bore to change the at least one parameter of the bore so as to have an in-process value equal to the final value or that has progressed from the initial value toward the final value; and performing the bore finishing iteration under control of the process parameters and measuring the in-process value at known axial locations in the bore; wherein the measured in-process values are automatically mathematically treated to determine an optimized set of values for the process parameters for a next bore finishing iteration for achieving a target value for the at least one parameter of the bore of the next iteration within specified limits - in that the optimized set of values for the process parameters for a next bore finishing iteration includes at least one parameter of a stroke of the reciprocation and a duration of the next iteration, and - in that the set of process parameters comprises at least one parameter of the finishing tool configured as a function of at least one predictive factor for changing the at least one parameter of the bore by a predetermined amount, and - by a step of automatically determining whether the at least one parameter of the bore changed during the iteration by at least the predetermined amount; and i. if yes, then continuing to use the at least one predictive factor; and ii. if no, then changing the at least one predictive factor for a subsequent iteration. i. if yes, then continuing to use the at least one predictive factor; and ii. if no, then changing the at least one predictive factor for a subsequent iteration.