  Primordial non-Gaussianity, in particular the coupling of modes with widely
different wavelengths, can have a strong impact on the large-scale clustering
of tracers through a scale-dependent bias with respect to matter. We
demonstrate that the standard derivation of this non-Gaussian scale-dependent
bias is in general valid only in the extreme squeezed limit of the primordial
bispectrum, i.e. for clustering over very large scales. We further show how the
treatment can be generalized to describe the scale-dependent bias on smaller
scales, without making any assumptions on the nature of tracers apart from a
dependence on the small-scale fluctuations within a finite region. If the
leading scale-dependent bias \Delta b \propto k^{\alpha}, then the first
subleading term will scale as k^{\alpha+2}. This correction typically becomes
relevant as one considers clustering over scales k >~ 0.01 h Mpc^{-1}.
