  Based on an explicit verification of the coupling matrix elements between the
1p1h and 2p2h states we propose a new method of selecting the most important
2p2h states responsible for fragmentation effects. In this way the
dimensionality of the problem is reduced, such that the computation becomes
feasible and the spreading of the strength is realistic, as verified by some
tests of convergence. Calculations in $^{208}$Pb show that due to sizable
mixing effects only about 50% of the total isoscalar giant dipole resonance
(ISGDR) $3\hbar\omega$ strength is located in the energy region between 20 and
25 MeV. This is the energy region which currently is available in experiment.
Even above 30 MeV we find about 10% of the total strength. This indicates that
the current experimantal evaluations of the ISGDR centroid energy may
significantly underestimate its value.
