  We study the frequency process $f_1$ of the block of 1 for a
$\varXi$-coalescent $\varPi$ with dust. If $\varPi$ stays infinite, $f_1$ is a
jump-hold process which can be expressed as a sum of broken parts from a
stick-breaking procedure with uncorrelated, but in general non-independent,
stick lengths with common mean. For Dirac-$\varLambda$-coalescents with
$\varLambda=\delta_p$, $p\in[\frac{1}{2},1)$, $f_1$ is not Markovian, whereas
its jump chain is Markovian. For simple $\varLambda$-coalescents the
distribution of $f_1$ at its first jump, the asymptotic frequency of the
minimal clade of 1, is expressed via conditionally independent shifted
geometric distributions.
