Hurewicz sets of reals without perfect subsets

We show that even for subsets X of the real line that do not contain perfect sets, the Hurewicz property does not imply the property S ₁(Γ, Γ), asserting that for each countable family of open γ-covers of X, there is a choice function whose image is a γ-cover of X. This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszyński and the second author, and implies that for C _P(X), the conjunction of Sakai's strong countable fan tightness and the Reznichenko property does not imply Arhangel'skiǐ's property α ₂.