We study a notion of 'o-amorphous' (in set theory without the axiom of choice) which bears the same relationship to 'o-minimal' as 'amorphous ' (studied in Truss, Ann. Pure Appl. Logic 73 (1995) 191-233) does to 'strongly minimal'. A linearly ordered set is said to be o-amorphous if its only subsets are ÿnite unions of intervals. This turns out to be a relatively straightforward case, and we can provide a complete 'classiÿcation', subject to the same provisos as in Truss (1995). The reason is that since o-amorphous is an essentially second-order notion, it corresponds more accurately to ℵ 0-categorical o-minimal, and our classiÿcation is thus very similar to the one given in (Pillay and Steinhorn, Trans. Amer. Math. Soc. 295 (1986) 565-592) for that case. More interesting structures arise if we replace 'interval' in the deÿnition by 'convex set', giving us the class of weakly o-amorphous sets. Here, in fact, there are so many examples that a complete classiÿcation seems out of the question. We illustrate some of the structures which these may exhibit, and classify them in certain instances not too far removed from the o-amorphous case.