Photon scattering experiments on the odd, deformed nuclei Dy-161,Dy-163 and Gd-157 provided detailed information on the excitation energies and transition probabilities of low-lying dipole excitations. In the case of the even-even nuclei Dy-162,Dy-164 in addition spins and parities of the excited states could be determined model independently by measuring the angular distributions and the linear polarization of the scattered photons using a Compton polarimeter. The results are compared with the systematics obtained for the neighboring even-even isotopes Dy-160 and Gd-156,Gd-158,Gd-160 in previous photon scattering experiments. Whereas in the odd Dy isotopes a concentration of dipole strength is observed, which fits nicely into the systematics of the orbital M1 mode, the dipole strength in Gd-157 is completely fragmented into about 90 transitions.