This chapter bounds the condition numbers of thestiffness matrix of operator-adapted wavelets within each subband (scale). These resulting bounds are characterized through weak alignment conditions between measurement functions and eigensubspaces of the underlying operator. In Sobolev spaces, these alignment conditions translate into approximate error estimates associated with variational splines andscattered data approximation. These estimates are established for the three primary examples, subsampled Diracs, Haar prewavelets, and local polynomials,of hierarchies of measurement functions in Sobolev spaces.