A quasi-perfect map is a continuous, closed function such that the preimage of every point is countably compact. An ambitious old problem due to van Douwen [1] is whether every first countable regular space of cardinality ≤c is a quasi-perfect image of a locally compact space. Here we construct locally compact, normal, quasi-perfect preimages for all stationary, co-stationary subsets of ω1. These subsets are ω1-compact but not σ-countably compact. Quasi-perfect preimages preserve these properties, and the preimages constructed here are all of cardinality b. This provides a new upper bound for the following problem:What is the least cardinality of a ZFC example of a locally compact,ω1-compact space that is not σ-countably compact?