We discuss certain covering
properties which are based on Michael’s notion of a cushioned collection. In
particular, we discuss property L of Bacon and certain variations on property L in
connection with isocompactness and the relationship between ℵ1-compactness and
the Lindelöf property. We then introduce property 𝜃L which is a common
generalization of property L and weak δ𝜃-refinability, and consider uses of this
property in similar connections.