The present paper considers the application of the Newton- Kantorovich and modified-gradient methods to the Ipswich data. The object is assumed to be an inhomogeneous lossy dielectric cylinder of arbitrary cross section. Both inverse-scattering methods are based on electric-field integral representations. The Newton- Kantorovich technique builds up the solution by solving successively the forward problem and a linear inverse problem. This method needs regularization, and we use either the identity operator or a gradient operator for regularization. The modified-gradient method is iterative, as is the Newton algorithm, but does not involve a linearization at each step of the nonlinear inverse problem. Results of inversions with both methods, on two known impenetrable targets, are discussed.