  We investigate the number of half-regular squares required to decompose a
non-negative $C^{k,\alpha}(\mathbb{R}^n)$ function into a sum of squares. Each
non-negative $C^{3,1}(\mathbb{R}^n)$ function is known to be a finite SOS in
$C^{1,1}(\mathbb{R}^n)$, and similar regularity-preserving SOS decompositions
have been studied by various authors. Our work refines existing techniques to
unify and build upon several known decomposition results, and moreover we
provide upper and lower estimates on the number of squares required for SOS
decompositions in $C^{k,\alpha}(\mathbb{R}^n)$.
