This paper presents a contrast source inversion method for microwave tomography with improved performance with respect to the popular multiplicative regularized contrast source inversion (MR-CSI) method when the contrast of the object under study is relatively high. More precisely, some shortcomings of MR-CSI which may prevent it from performing adequately on higher contrast objects are outlined. The proposed method does not suffer from such shortcomings, but necessitates the tuning of parameters. However, a unique set of parameters can be used in a wide variety of experimental conditions related to a given application. Simple guidelines to determine their values are provided.