Summary: We show that the dual effectively monotone span of a simple closed curve \(X\) in the plane does not exceed the infimum of the set of positive numbers \(m\) such that a chain with mesh \(m\) covers \(X\). We also include a short direct proof of a known inequality \(\sigma_0(0) \leq\varepsilon(X)\), where \(X\) is a continuum.