Surface asperities, such as roughness characteristics, are reduced or otherwise mitigated via the control of surface regions including the asperities in different regimes. In accordance with various embodiments, the height of both high-frequency and low-frequency surface asperities is reduced by controlling characteristics of a surface region under a first regime to flow material from the surface asperities. A second regime is implemented to reduce a height of high-frequency surface asperities in the surface region by controlling characteristics of the surface region under a second regime to flow material that is predominantly from the high-frequency surface asperities, the controlled characteristics in the second regime being different than the controlled characteristics in the first regime. Such aspects may include, for example, controlling melt pools in each regime via energy pulses, to respectively mitigate/reduce the asperities.