Tightness in products of fans and psuedo-fans

Give κ the discrete topology and ω + 1 the order topology. The κ-fan Fκ is the quotient space obtained by identifying the nonisolated points of κ × (ω + 1) to a point ∞. We investigate the tightness of products of the form Fκ × Fλ, where λ ⩽ κ. Some of our results are t(Fκ × Fλ) ⩽ λω, t+(Fℵω × Fℵω) ⩽ ℵω, and a new connection between the tightness of Fκ × Fλ and the failure of ⩽ κ-cwH in first countable < κ-cwH spaces.