This electron-density study on corundum (alpha-Al2O3) is part of the Multipole Refinement Project supported by the IUCr Commission on Charge, Spin and Momentum Densities. For this purpose, eight different data sets (two experimental and six theoretical) were chosen from which the electron density was derived by multipolar refinement (using the MOLLY program). The two experimental data sets were collected on a conventional CAD4 and at ESRF, ID11 with a CCD detector, respectively. The theoretical data sets consist of static, dynamic, static noisy and dynamic noisy moduli of structure factors calculated at the Hartree-Fock (HF) and density functional theory (DFT) levels. Comparisons of deformation and residual densities show that the multipolar analysis works satisfactorily but also indicate some drawbacks in the refinement. Some solutions and improvements during the refinements are proposed like contraction or expansion of the inner atomic shells or increasing the order of the spherical harmonic expansion.