  We analytically compute subsystem action complexity for a segment in the BTZ
black hole background up to the finite term, and we find that it is equal to
the sum of a linearly divergent term proportional to the size of the subregion
and of a term proportional to the entanglement entropy. This elegant structure
does not survive to more complicated geometries: in the case of a two segments
subregion in AdS$_3$, complexity has additional finite contributions. We give
analytic results for the mutual action complexity of a two segments subregion.
