These rearrangements all proceed via a species conrtaining a three membered ring (readily formed under kinetic conditions, as the entropic cost of forming such a ring is very low). These rings are highly strained (as all the substituents are eclipsed) so are then readily opened in the course of the rearrangement. (This removal of ring strain may in some cases actually provide the driving force for the rearrangement.)

Favorskii

The Favorskii is a useful reaction for ring contraction.

Payne Rearrangement

If a bulky nucleophile is present it will attack the less hindered of the two epoxides. For example;

Entropically favoured

Steps like the second step here which involve loss of a stable gaseous molecule (N2 is possibly the best of all as it is highly inert and has a lot of bond energy - this makes compounds that are able to lose N2 rather explosive!) are very favourable entropically (increase of disorder!) and therefore not uncommon in rearrangements, for hich they can provide the thermodynamic driving force.