For understanding the operation of perovskite solar cells and light-emitting diodes, knowledge of the dielectric properties is indispensable. The dielectric properties of perovskites are frequency dependent due to the presence of moving ions, which complicates the interpretation of impedance spectra. Using Au/CsPbI2Br/Au capacitors with varied layer thickness as a model system, we demonstrate that in the dark, an extended Maxwell circuit consistently describes the impedance data. From the thickness dependence of the resistivities, both the electronic and ionic conductivities are obtained, whereas the combination of electronic and ionic capacitances with the characteristic frequencies for space-charge formation determines the ion diffusion coefficient and ion density. At low frequencies, a slow transient process with a fixed time constant of ∼0.1 s occurs, governed by the electronic conductivity, being independent of illumination strength and sample thickness. As a possible mechanism, we propose the spatial reorganization of ions within the ion accumulation layer at the electrode/perovskite interface.