The effects of microgravity and of axial magnetic fields on the micro- and macrosegregation in Si floating-zone crystals are compared. Whereas in the absence of radio frequency (RF) heating thermocapillary and buoyancy convection contribute to macrosegregation, thermocapillary convection leads to dopant striations due to its time dependency. Consequently, floating-zone growth under microgravity (mug) is not capable of suppressing the formation of striations, but due to the reduced mixing of the melt the striation intensity is modestly decreased and the axial macrosegregation is changed. The application of an axial magnetic field up to 0.5 T under terrestrial growth conditions allows a suppression of striations together with a change in the axial macrosegregation. It is, however, detrimental to the radial uniformity of the dopant concentration by producing a non-facet ''core'' in the crystal, with the core diameter depending on the magnetic induction.