The economics of short-rotation pulpwood plantations of Eucalyptus globulus as a coppice crop are influenced by stump survival and subsequent coppice growth rates. This study revealed significant genetic diversity in coppicing traits, both within and between subraces, following felling in a progeny trial after 9 years of growth. A total of 67% of trees coppiced after 14 months, but subraces varied from 43 to 73%. Heritabilities for coppice success (0.07) and subsequent growth (0.16–0.17) were low but statistically significant. Strong genetic correlation between presence/absence of coppice, the number of stems coppicing from the stump and modal coppice height, indicate that selection is possible by using the binary trait. The ability of a tree to coppice was genetically correlated with tree growth prior to felling (rg = 0.61) and with nursery-grown seedling traits, where large genetic differences were observed in the development of lignotubers. Coppicing was genetically correlated with the number of nodes with lignotubers (rg = 0.66) and seedling stem diameter at the cotyledonary node (rg = 0.91). These traits were uncorrelated with later age growth and with each other. The results suggest that coppicing is influenced by three independent mechanisms—lignotuber development, enlargement of the seedling stem at the cotyledonary node and vigorous growth—which enhance ability to survive catastrophic damage, and indicate that both lignotuber and coppice development can be altered by both natural and artificial selection.