  The Kondo scale TK for impurity systems is expected to guarantee universal
scaling of physical quantities. However, in practice, not every definition of
TK necessarily supports this notion away from the strict scaling limit.
Specifically, this paper addresses the role of finite bandwidth D in the
strongly-correlated Kondo regime. For this, various theoretical definitions of
TK are analyzed based on the inverse magnetic impurity susceptibility at zero
temperature. While conventional definitions in that respect quickly fail to
ensure universal Kondo scaling for all D, this paper proposes an altered
definition of TK_{sc} that allows universal scaling of dynamical or thermal
quantities for a given fixed Hamiltonian. If the scaling is performed with
respect to an external parameter which directly enters the Hamiltonian, such as
magnetic field, the corresponding TK_{sc;B} for universal scaling differs, yet
becomes equivalent to TK_{sc} in the scaling limit. The only requirement for
universal scaling in the full Kondo parameter regime with a residual error of
less than 1% is a well-defined isolated Kondo feature with TK < 0.01D. By
varying D over a wide range relative to the bare energies of the impurity, for
example, this allows a smooth transition from the Anderson to the Kondo model.
