  We give a shorter proof of a slightly weaker version of a theorem of Nets
Katz and the author. We prove that if a set of $L$ lines in $\mathbb{R}^3$
contains at most $L^{1/2}$ lines in any low degree algebraic surface, then the
number of $r$-rich points is at most $C_\epsilon L^{(3/2) + \epsilon} r^{-2}$.
Nets and I used this estimate to prove a distinct distance estimate for points
in the plane. With the slightly weaker theorem in this paper, we get a slightly
weaker distinct distance estimate: any set of $N$ points in $\mathbb{R}^2$
determines at least $c_\epsilon N^{1 - \epsilon}$ distinct distances.
