Summary: The standard dynamic procedure is based on the scale-invariance assumption that the model coefficient \(C\) is the same at the grid and test-filter levels. In many applications this condition is not met. We consider the case when the filter-length, Delta, approaches the Kolmogorov scale, \(\eta\), and \(C(\Delta\to\eta)\to\dot 0\). Using filtered direct numerical simulation data, we show that the standard dynamic model yields the coefficient corresponding to the test-filter scale (\(\alpha\Delta\)) instead of the grid scale (\(\Delta\)). Several approaches to account for scale dependence in the dynamic Smagorinsky model are considered, and the most robust of these is tested in large eddy simulation of forced isotropic turbulence at various Reynolds numbers.