In this paper, we continue the exploration of possibilities, limitations, and methodological problems of the studies based on measurements of the nuclear spin relaxation rates running via the scalar relaxation of the second kind (SC2) mechanism. The attention has been focused on the C-13-Br-79 and C-13-Br-81 systems in organic bromo compounds, which are characterized by exceptionally small differences of Larmor frequencies, Delta omega(CBr), of the coupled nuclei. This unique property enables experimental observation of longitudinal SC2 relaxation of C-13 nuclei, which makes investigation of the SC2 relaxation rates an attractive experimental method of determination of spin spin coupling constants and relaxation rates of quadrupole bromine nuclei, both types of parameters being hardly accessible by direct measurements. A careful examination of the methodology used in SC2 relaxation studies of carbon bromine systems reveals, however, some disturbing facts that could burden the results with systematic inaccuracies. Namely, the way of calculating the Larmor frequency differences between C-13 and bromine isotopes, Delta omega CBr, may cause some reservations. In this work, the values of Br-79 and Br-81 magnetogyric ratios have been rechecked using bromine NMR data for the KBr center dot Kryptofix 222 complex in acetonitrile solution and the results of the advanced calculations of the magnetic shielding of the bromine nucleus in the Br anion. Moreover, it has been pointed out that in the case of 13C-79Br, the magnetic shielding of the bromine nucleus in the investigated molecule must not be neglected during the calculation of the Delta omega(CBr) parameter. Some recommendations concerning the exploitation of available theoretical methods to calculate bromine shielding constants for bromo compounds have also been formulated, keeping in mind relativistic effects.