Continuing studies based on measurements of the nuclear spin relaxation rates running via the SC2 mechanism (scalar relaxation of the second kind), we present in this work the results obtained for three molecules: 9-bromotriptycene, 1,3,5-tribromobenzene, and 1-(2-bromoethynyl)-4-ethynylbenzene in which C-Br bond and one of C-H bonds are collinear. Separation of saturation-recovery or inversion-recovery curves of C-13 NMR signals of bromine-bonded carbons in the investigated compounds on two components has provided the longitudinal SC2 relaxation rates of these carbons in Br-79- and Br-81-containing isotopomers. These data have enabled experimental determination of the bromine-carbon spin-spin coupling constants and relaxation rates of quadrupole bromine nuclei, hardly accessible by direct measurements. At the same time the rotational diffusion parameters describing the reorientation of the C-Br vectors have been determined for the investigated molecules on the basis of the dipolar relaxation of protonated carbons. These diffusion parameters are crucial for interpretation of the bromine relaxation rates. The values of the indirect (1)J(C-13,Br-79) coupling constants, magnetic shielding of carbon nuclei and quadrupole coupling constants of bromines, determined for the investigated compounds, have been compared with the results of the theoretical calculations which take into account relativistic effects. The origin of some divergences between the results obtained by different methods has been discussed.