This paper describes a self-consistent axisymmetric stationary MHD model of the Jovian magnetosphere, in which both the centrifugal force and the pressure gradients exerted on the plasma are taken into account. The outer boundary condition is chosen so as to represent the dayside (noon meridian). The plasma distribution within the magnetosphere is represented by two Maxwellian components; a cold plasma (several tens of eV) produced at the orbit of Io and diffusing outward under centrifugally driven interchange instability, and a hot (30 keV) low-density plasma, originating from the outer regions of the magnetosphere and diffusing inward in response to it. Outside the Io torus, this process is assumed to be sufficiently rapid that the amount of particles of each population per unit flux tube is independent of distance. The self-consistent solution to the model, with input parameters suitable for the Voyager 1 encounter, is presented and compared to observations. It is found to produce very satisfactorily the large-scale features of the dayside magnetic field, plasma density, and plasma pressure, thus supporting the relevance of the plasma distribution that was assumed as input to the model. Among the main conclusions, the pressure gradients are found to constitute the major source of azimuthal currents, thus producing, at all distances, at least 68% of the total current (integrated over latitude) per unit radial distance. The centrifugal current is of secondary importance, although its distribution is more closely confined to the equator. Several runs of the model made with different outer boundary conditions have also permitted study of the compressibility of the magnetosphere, thus showing that due to the presence of high beta plasma within it, the Jovian magnetosphere is much more sensitive to variations of the solar wind pressure than is the terrestrial magnetosphere, in accordance with the observed large variability of the Jovian magnetopause location.