Observations of Jupiter’s gravity field by Juno have revealed surprisingly low values for the high-order gravitational moments, considering the abundances of heavy elements measured by Galileo 20 years ago. The derivation of recent equations of state for hydrogen and helium, which are much denser in the megabar region, exacerbates the conflict between these two observations. In order to circumvent this puzzle, current Jupiter model studies either ignore the constraint from Galileo or invoke an ad hoc modification of the equations of state. In this paper, we derive Jupiter models that satisfy constraints of both Juno and Galileo. We confirm that Jupiter’s structure must encompass at least four different regions: an outer convective envelope, a region of compositional and thus entropy change, an inner convective envelope, an extended diluted core enriched in heavy elements, and potentially a central compact core. We show that in order to reproduce Juno and Galileo observations, one needs a significant entropy increase between the outer and inner envelopes and a lower density than for an isentropic profile, which is associated with some external differential rotation. The best way to fulfill this latter condition is an inward-decreasing abundance of heavy elements in this region. We examine in detail the three physical mechanisms that can yield such a change of entropy and composition: a first-order molecular-metallic hydrogen transition, immiscibility between hydrogen and helium, or a region of layered convection. Given our present knowledge of hydrogen pressure ionization, a combination of the two latter mechanisms seems to be the most favored solution.