  The Kiselev model describes a black hole surrounded by a fluid with equations
of state $p_r/\rho=-1$ and $p_t/\rho=(3w+1)/2$ respectively in radial and
tangential directions. It has been extensively studied in the parameter region
$-1<w<-1/3$. If one rids off the black hole and turns to the region $-1/3<w<0$,
i.e. $p_t>0$, then a new horizon of black hole type will emerge. This case has
been mentioned in Kiselev's pioneer work but seldom investigated in the
literature. Referring to it as reduced Kiselev black hole, we revisit this case
with attention to its causal structure, thermodynamics, shadow cast and
weak-field limit. An alternative interpretation and extensions of the black
hole are also discussed.
