  Let $X$ be Banach space which is not super-reflexive. Then, for each $n\ge1$
and $\varepsilon>0$, we exhibit metric embeddings of the Laakso graph
$\mathcal{L}_n$ into $X$ with distortion less than $2+\varepsilon$ and into
$L_1[0,1]$ with distortion $4/3$. The distortion of an embedding of
$\mathcal{L}_2$ (respectively, the diamond graph $D_2$) into $L_1[0,1]$ is at
least $9/8$ (respectively, $5/4$).
