Based on an explicit verification of the coupling matrix elements betw
een the 1p1h and 2p2h states we propose a new method of selecting the
most important 2p2h states responsible for fragmentation effects. In t
his way the dimensionality of the problem is reduced, such that the co
mputation becomes feasible and the spreading of the strength is realis
tic, as verified br some tests of convergence. Calculations in Pb-208
show that due to sizeable mixing effects only about 50% of the total i
soscalar giant dipole resonance (ISGDR) 3 (h) over bar w strength is l
ocated in the energy region between 20 and 25 MeV. This is the energy
region which currently is available in experiment. Even above 30 MeV w
e find about 10% of the total strength. This indicates that the curren
t experimental evaluations of the ISGDR centroid energy may significan
tly underestimate its value.