In this paper we construct the subset of modes on S 7 that are relevant in the compactification of eleven-dimensional supergravity on a squashed S 7 when restricted to the sector that comprises singlets under the Sp(1) × Sp(2) isometry of the squashed sphere. Some of the properties of these modes, connected to the transition from the round S 7 to the squashed S 7 , are analysed in detail. Special features of the Rarita-Schwinger operator, described in earlier work by Buchdahl, are explained and related to properties of the squashed S 7 operator spectrum obtained in previous work by the authors. We then discuss how the singlet modes give rise to supermultiplets in the leftsquashed case, the phenomenon of de-Higgsing, and what happens to the AdS 4 fields in these supermultiplets under an orientation reversal ("skew-whiffing") of the squashed S 7 . Finally, we consider the possible choices of boundary conditions that appear for some of these fields in AdS 4 in the case of the right-squashed non-supersymmetric compactification, and how these choices may affect the stability of the gravity theory.