  A $t$-bar visibility representation of a graph assigns each vertex up to $t$
horizontal bars in the plane so that two vertices are adjacent if and only if
some bar for one vertex can see some bar for the other via an unobstructed
vertical channel of positive width. The least $t$ such that $G$ has a $t$-bar
visibility representation is the bar visibility number of $G$, denoted by
$b(G)$. We show that if $H$ is a spanning subgraph of $G$, then $b(H)\le
b(G)+1$. It follows that $b(G)\le \lceil n/6\rceil+1$ when $G$ is an $n$-vertex
graph. This improves the upper bound obtained by Chang et al. (SIAM J. Discrete
Math. 18 (2004) 462).
