  In the standard diffusive picture for transport of cosmic rays (CRs), a
gradient in the CR density induces a typically small, dipolar anisotropy in
their arrival directions. This has been widely advertised as a tool for finding
nearby sources. However, the predicted dipole amplitude at TeV and PeV energies
exceeds the measured one by almost two orders of magnitude. Here, we critically
examine the validity of this prediction which is based on averaging over an
ensemble of turbulent magnetic fields. We focus (1) on the deviations of the
dipole in a particular random realisation from the ensemble average and (2) the
possibility of a misalignment between the regular magnetic field and the CR
gradient. We find that if the field direction and the gradient direction are
close to $\sim 90^\circ$, the dipole amplitude is considerably suppressed and
can be reconciled with observations, which sheds light on a long-standing
problem. Furthermore, we show that the dipole direction in general does not
coincide with the gradient direction, thus hampering the search for nearby
sources.
