We show that for the pretzel knots Kk=P(3,−3,−2k−1)$K_k=P(3,-3,-2k-1)$, the n$n$‐fold cyclic‐branched covers are L‐spaces for all n⩾1$n\geqslant 1$. In addition, we show that the knots Kk$K_k$ with k⩾1$k\geqslant 1$ are quasi‐positive and slice, answering a question of Boileau–Boyer–Gordon. We also extend results of Teragaito giving examples of two‐bridge knots with all L‐space cyclic‐branched covers to a family of two‐bridge links. [ABSTRACT FROM AUTHOR]