Dobrinen, Hathaway and Prikry studied a forcing âÎș consisting of perfect trees of height λ and width Îș where Îș is a singular λ-strong limit of cofinality λ. They showed that if Îș is singular of countable cofinality, then âÎș is minimal for Ï-sequences assuming that Îș is a supremum of a sequence of measurable cardinals. We obtain this result without the measurability assumption.Prikry proved that âÎș is (Ï, Îœ)-distributive for all Îœ < Îș given a singular Ï-strong limit cardinal Îș of countable cofinality, and Dobrinen et al. asked whether this result generalizes if Îș has uncountable cofinality. We answer their question in the negative by showing that âÎș is not (λ, 2)-distributive if Îș is a λ-strong limit of uncountable cofinality λ and we obtain the same result for a range of similar forcings, including one that Dobrinen et al. consider that consists of pre-perfect trees. We also show that âÎș in particular is not (Ï, ·, λ+)-distributive under these assumptions.While developing these ideas, we address natural questions regarding minimality and collapses of cardinals.