  We analyze the question of which motivic homotopy types admit smooth schemes
as representatives. We show that given a pointed smooth affine scheme $X$ and
an embedding into affine space, the affine deformation space of the embedding
gives a model for the ${\mathbb P}^1$ suspension of $X$; we also analyze a host
of variations on this observation. Our approach yields many examples of
${\mathbb A}^1$-$(n-1)$-connected smooth affine $2n$-folds and strictly
quasi-affine ${\mathbb A}^1$-contractible smooth schemes.
