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Abstract. Let X be a locally compact, completely regular, Hausdorff space, and let K(X) be the lattice of compactifications of X. Conditions on K(X) and an internal condition are obtained which characterize when X has all compact metric spaces as remainders.

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ABSTRACT. Let X be a completely regular, Hausdorff space and let R be the set of points in X which do not possess compact neighborhoods. Assume R is compact. If X has a compactification with a countable remainder, then so does the quotient X/R, and a countable compactificatlon of X/R implies one for X-R. A characterization of when X/R has a compactification with a countable remainder is obtained. Examples show that the above implications cannot be reversed.