We have developed 1D analytic and 2D fully electromagnetic models of radial transmission-line impedance transformers. The models have been used to quantify the power-transport efficiency and pulse sharpening of such transformers as a function of voltage pulse width and impedance profile. For the cases considered, we find that in the limit as Γ→0 (where Γ is the ratio of the pulse width to the one-way transit time of the transformer), the transport efficiency is maximized when the impedance profile is exponential. As Γ increases from zero, the optimum profile gradually deviates from an exponential. A numerical procedure is presented that determines the optimum profile for a given pulse shape and width. The procedure can be applied to optimize the design of impedance transformers used in petawatt-class pulsed-power accelerators.