  Two permutations are similar if they have the same length and the same
relative order. A collection of $r\ge2$ disjoint, similar subsequences of a
permutation $\pi$ form $r$-twins in $\pi$. We study the longest guaranteed
length of $r$-twins which are tight in the sense that either each twin alone
forms a block or their union does. We address the same question with respect to
a random permutation.
