Graded algebras can be deformed in non-homogeneous ways to create PBW deformations. Over a field K, a deformation U of a graded K-algebra A is said to be of PBW type if the graded algebra associated to U is isomorphic to A. It has been shown for Koszul and N-Koszul algebras that the deformation is PBW if and only if the relations of U satisfy a Jacobi type condition. I will discuss recent work with Brad Shelton (U. of Oregon) extending these results to an arbitrary graded K-algebra, using the notion of central extensions of algebras and a homological constant attached to A which we call the complexity of A.