  We generalize the familiar notion of a Whitehead move from Culler and
Vogtmann's Outer space to the setting of deformation spaces of G-trees.
Specifically, we show that there are two moves, each of which transforms a
reduced G-tree into another reduced G-tree, that suffice to relate any two
reduced trees in the same deformation space. These two moves further factor
into three moves between reduced trees that have simple descriptions in terms
of graphs of groups. This result has several applications.
