  Let $B$ and $R$ be point sets (of {\em blue} and {\em red} points,
respectively) in the plane, such that $P:=B\cup R$ is in general position, and
$|P|$ is even. A line $\ell$ is {\em balanced} if it spans one blue and one red
point, and on each open halfplane of $\ell$, the number of blue points minus
the number of red points is the same. We prove that $P$ has at least $\min
\{|B|,|R|\} $ balanced lines. This refines a result by Pach and Pinchasi, who
proved this for the case $|B|=|R|$.
