A radiation-treatment planning apparatus accesses information regarding a treatment target and at least one operational parameter pertaining to a physical characteristic of a given radiation-treatment platform. The apparatus also accesses information regarding a candidate treatment plan using the given platform. The apparatus then optimizes the candidate treatment plan by permitting, temporarily, discontinuities of the at least one operational parameter as between adjacent ones of a plurality of control points to thereby yield an optimized treatment plan. By one approach, this operational parameter can comprise a speed at which a collimator aperture can be changed. In such a case, the aforementioned discontinuities can comprise discontinuities with respect to the speed at which this aperture can be changed. So configured, these teachings will accommodate temporarily permitting speeds that are too fast to be actually performed by the given radiation-treatment platform.