An imp can regenerate itself.

... imps ... little creatures of two feet high that could gambol and jump prodigiously; ...
The Charwoman's Shadow, by Lord Dunsany An 'imp' is an off-shoot or cutting. Thus an 'ymp tree' was a grafted tree, or one grown from a cutting, not from seed. 'Imp' properly means a small devil, an off-shoot of Satan, but the distinction between goblins or bogles and imps from hell is hard to make, and many in the Celtic countries as well as the English Puritans regarded all fairies as devils. The fairies of tradition often hover uneasily between the ghostly and the diabolic state.
A Dictionary of Fairies, by Katharine Briggs