Controversial aspects of the conventional and widely used concept of the integral vortex strength are briefly discussed. The strength of a vortex is usually calculated as the circulation along the vortex boundary, or equivalently due to Green's theorem, as the surface integral of vorticity over the planar vortex cross section. However, the local effect of an arbitrary "superimposed shear" is fully absorbed by vorticity what makes the circulation a shear-biased vortex characteristic. The present paper shows that different vortex-strength models can be derived on the basis of different local vortex intensities proposed in the literature. The outcome of these models naturally differs, even for an ideally axisymmetric vortex. Three different vortex-strength models are compared and discussed by examining the unsteady Taylor vortex.