Numerical simulations of the flux-free Meissner state and the partly flux-filled critical state of a thin, current-carrying type-II superconductor strip shielded by a soft-magnetic environment of restricted geometry are performed, calling upon the ANSYS finite-element software program and exploiting magnetostatic-electrostatic analogues. The distribution of the static magnetic field around the superconductor strip, the distribution of the sheet current in the strip, and the maximum total transport current carried by the strip are established for two practically relevant magnet configurations and a range of magnetic permeabilities. The predictions of the simulations are qualitatively in line with previous analytical and numerical results concerning idealized shields; they demonstrate the existence of non-dissipative overcritical states associated with substantial redistributions of the sheet current towards the centre of the strip and significant enhancements of the total loss-free current that can be carried by the strip for both the introduced concave and, respectively, convex magnetic cavity, however with a bias in favour of the latter type of environment. The shielding effect is highly sensitive to the distance between the edges of the strip and the magnets and, unlike the case for magnets of semi-infinite extent, exhibits slow saturation with increasing values of the magnetic permeability. Hysteretic ac losses suffered by the magnetically shielded strip in the periodically changing, partly flux-filled critical state drastically wane when the magnetic permeability augments.