It is demonstrated by a fluctuation analysis based on the assumption of a Wigner distribution fur the nuclear level spacings and of a Porter-Thomas distribution for the transition strengths thai significant parts nf the dipole strength excited in photon scattering experiments in heavy, deformed odd-mass nuclei are hidden in the background of the experimental spectra. With this additional strength, the heretofore claimed severe reduction af the B(M1) scissors mode strength in odd-mass nuclei compared to the one in neighboring even-even nuclei disappears.