  We consider the torus reduction of heterotic supergravity in the presence of
four-derivative corrections. In particular, the reduction on $T^n$ generically
leads to a half-maximal supergravity coupled to $n$ vector multiplets, and we
show that it is consistent to truncate out said vector multiplets. This is done
by the analysis of both the bosonic equations of motion and the Killing spinor
equations. As an application of the consistent truncation, we examine the
four-derivative corrected BPS black string that reduces to a black hole in
minimal nine-dimensional supergravity.
