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We show that for any two values $\alpha, \beta >0 $ for which$\alpha+\beta>1$ then there is a value $N$ so that for all $n \geq N$ thefollowing holds. For any binary phylogenetic tree $T$ on $n$ leaves there is aset of $\lfloor n^\alpha \rfloor$ characters that capture $T$, and for whicheach character takes at most $\lfloor n^\beta \rfloor$ distinct states. Here`capture' means that $T$ is the unique perfect phylogeny for these characters.Our short proof of this combinatorial result is based on the probabilisticmethod.

Capturing a phylogenetic tree when the number of character states varies with the number of leaves