We present results from the modeling of ground deformation and microgravimetric data recorded at Campi Flegrei in order to assess the causative phenomena of caldera unrest between 1981 and 2001. We find that residual gravity changes during ground uplift (1982--1984) are indicative of mass changes in a hybrid of magmatic and hydrothermal sources. During deflation between 1985 and 2001, the inversion of gravity residuals for a single source does not provide convincing results. We then performed the joint inversion of gravity and deformation data for multiple spherical sources and refined source parameters by finite element modeling in order to mitigate against limitations of the analytical solutions. The data recorded during inflation and rapid deflation may be best explained by mass and pressure changes in a deep magmatic source at about 5 km depth and a shallow (2 km deep) hydrothermal source. Both sources contribute equally to the gravity changes observed between 1982 and 1984; the contemporary uplift appears to be mainly caused by the shallow source. The subsequent deflation is dominated by a pressure decrease in the hydrothermal source; the magmatic source contributes chiefly to the observed gravity changes. Pressure and density variations within multiple shallow-seated hydrothermal sources provide acceptable fits to the deflation and accompanying gravity changes recorded since 1988. These shallow level dynamics also appear to trigger spatially and temporarily random short-term reversals of the overall mode of ground subsidence since 1985. Our analysis does not support the idea of magmatic contributions to these short-lived periods of inflation.