Let X be Banach space which is not super-reflexive. Then, for each n ≥ 1 and ε > 0, we exhibit metric embeddings of the Laakso graph Ln into X with distortion less than 2 + ε and into L1[0, 1] with distortion 4/3. The distortion of an embedding of L2 (respectively, the diamond graph D2) into L1[0, 1] is at least 9/8 (respectively, 5/4).
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