A new Wallman-type ordered compactification γ ∘ X is constructed using maximal C Z -filters (which have filter bases obtained from increasing and decreasing zero sets) as the underlying set. A necessary and sufficient condition is given for γ ∘ X to coincide with the Nachbin compactification β ∘ X ; in particular γ ∘ X = β ∘ X whenever X has the discrete order. The Wallman ordered compactification ω ∘ X equals γ ∘ X whenever X is a subspace of R n . It is shown that γ ∘ X is always T 1 , but can fail to be T 1 -ordered or T 2 .