Given a compact Polish space E and the hyperspace of its compact subsets K(E), we consider G δ σ-ideals of compact subsets of E. Solecki has shown that any σ-ideal in a broad natural class of G δ ideals can be represented via a compact subset of K(E); in this article we examine the behaviour of G δ subsets of E with respect to the representing set. Given an ideal I in this class, we construct a representing set that recognises a compact subset of E as being "small" precisely when it is in I, and recognises a G δ subset of E as being "small" precisely when it is covered by countably many compact sets from I.2000 Mathematics Subject Classification. 03E15, 28A05, 54H05.

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