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I investigate the scattering properties of transformation devices as the impedance matching criteria are altered. Starting from an analysis of traditional impedance calculations, we see how to preserve the cloak's "steering" refractive index profile whilst adjusting the "scattering" impedance profile. Results are presented for transformation devices in a cylindrical geometry, but the lessons apply to both simpler and more complicated transformation devices. One technique used here is the use of impulsive field inputs, so that scattered fields are more easily distinguished from non-scattered fields. A two-axis continuous range of impedance profiles is shown to cover the three most important cases. This range is investigated numerically, with the summed scattering field being used as an indicator of device performance. We see that the standard "$\kappa$-medium" case where $\epsilon=\mu$ gives best performance, but with different rescalings giving different levels of deterioration.&#13;