  Let $T$ be a positive closed current of bidimension $(1,1)$ with unit mass on
the complex projective space $\mathbb P^2$. For $\alpha > 2/5$ and $\beta =
(2-2\alpha)/3$ we show that if $T$ has four point with Lelong number greater
than $\alpha$, the upper level set $E_{\beta}^+ (T)$ of points of $T$ with
Lelong number strictly larger than $\beta$ is contained within a conic with the
exception of at most one point.
