Results are presented from experiments on studying the compactness of compression of imploding nested foam-wire loads at currents of up to 4 MA at the Angara-5-1 facility. The degree of pinch compression was estimated from the dynamics of the spatial distribution of the current (magnetic field) and the shape of the soft X-ray pulse. The load consisted of nested cascades, one of which being a wire array and the other being a hollow or solid low-density cylinder made of agar-agar foam with a wall thickness of 100-200 mu m. In some experiments, one of the cascades was made of C20H17O6 solid-state organic acid foam. The radial distribution of the magnetic field inside the nested cascades of the imploding foam-wire load (both between the cascades and inside the inner cascade) was measured using tiny magnetic probes. The measured radial distributions of the magnetic field are compared with the magnetic field configuration calculated using a one-dimensional MHD code simulating the implosion of a nested foam-wire load. It is shown that the spatial structure of the current and magnetic field during the implosion of such a load is determined by the development of supersonic and subsonic magnetized plasma flows in its cascades. The specific features of pinch formation and methods for the compensation of the nonsimultaneous pinch compression between the anode and the cathode (the zipper effect) during the implosion of a nested foam-wire load are analyzed.