"Nearly metacompact spaces"

We show that regular countably compact nearly metaLindel\"of spaces are compact. That nearly metacompact radial spaces are metaLindel\"of. That every space can be embedded as a closed subspace of a nearly metacompact space. We give an example of a Hausdorff countably compact, nearly metaLindel\"of space that is not compact, and a Hausdorff, nearly metacompact space which is not irreducible.