We have analyzed magnetization measurements in a series of composition-related Ni-Mn-Ga shape-memory alloys. It is shown that the magnetocaloric effect in the vicinity of the martensitic transition mainly originates from two different contributions: ~i! magnetostructural coupling on the mesoscopic scale between the magnetic moments and the martensitic variants, which is also responsible for the magnetic shape-memory effect and ~ii! the microscopic spin-phonon coupling which gives rise to the shift of the transition temperature with the applied magnetic field. The relative importance of these two contributions has been shown to vary with composition, which is suitably expressed through the average number of valence electrons per atom e/a. In alloys with a large difference between the Curie and martensitic transition temperatures (e/a.7.5), mesoscopic coupling is dominant and a negative giant magnetocaloric effect ~increase of temperature by adiabatic demagnetization! is induced at moderate applied fields. In contrast, in alloys when these temperatures are very close to one another (e/a.7.7), the microscopic coupling is the most relevant contribution and gives rise to a positive giant effect.