We investigate the performance of the Skyrme energy-density functional with respect to magnetic modes, checking in particular the impact of the spin-orbit and spin-spin interaction. Test cases are the low-energy M1 excitations in Pb208 treated within the self-consistent random-phase approximation based on the Skyrme energy-density functional. We scan a large variety of Skyrme parametrizations to find out which parameters of the functional have strongest correlations with M1 properties. We explore a simple method of the modification of the spin-related parameters, which delivers a better description of M1 excitations while basically maintaining the good description of ground-state properties.