  A method for deforming C*-algebras is introduced, which applies to
C*-algebras that can be described as the cross-sectional C*-algebra of a Fell
bundle. Several well known examples of non-commutative algebras, usually
obtained by deforming commutative ones by various methods, are shown to fit our
unified perspective of deformation via Fell bundles. Examples are the
non-commutative spheres of Matsumoto, the non-commutative lens spaces of
Matsumoto and Tomiyama, and the quantum Heisenberg manifolds of Rieffel. In a
special case, in which the deformation arises as a result of an action of
R^{2d}, assumed to be periodic in the first d variables, we show that we get a
strict deformation quantization.
