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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 ajump-hold process which can be expressed as a sum of broken parts from astick-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, whereasits jump chain is Markovian. For simple $\varLambda$-coalescents thedistribution of $f_1$ at its first jump, the asymptotic frequency of theminimal clade of 1, is expressed via conditionally independent shiftedgeometric distributions.

On the size of the block of 1 for $\varXi$-coalescents with dust