GMN,
Reducing power is usually the second step, after downtilt : when the downtilt just can’t fix the overshooting problem, then the optimizer must (often against its own instinct) reduce the TX POWER of the cell.
The downtilt reduces the cell coverage quite neatly (the cell border are sharper), yet it increases the indoor coverage nearby the cell.
The power decrease will attenuate the power in the whole cell range, and the actual cell range is not “sharper” than before the power attenuation.
Cheers,
pix