During any image segmentation process, two distinct tasks are performed - recognition and delineation. Recognition consists of the searching phase which roughly identifies a particular object of interest among other neighboring structures present in the image. Delineation consists of precisely defining the spatial extent of the object region. Well designed interactive segmentation methods, such as live wire (LW) and snakes, exploit the synergy between the user knowledge (for recognition) and the underlying computer processing done automatically (for delineation). We present in this paper two new methods, referred to as iterative live wire and live snake, for interactive 3D segmentation of medical images. In both methods, the segmentation initiated by the LW or snake method is propagated under user control to subsequent slices by projecting the anchor points. In iterative LW (ILW), the LW segments are iteratively updated in the new slice by selecting the mid points of previous LW segments as new anchor points. In live snake (LS), the snake method is first applied in the new slice for the projected anchor points and ended with an application of ILW. The methods have been evaluated on 30 3D MRI data sets of the breast. The results indicate that, on average, far fewer number of user interventions during segmentation and anchor point specification are needed by using the new methods than by using snakes propagation or live wire. The ILW segmentations are slightly more accurate, with statistical significance (P<0.01), than LS segmentations, and the former are more efficient than the latter (P<0.03), both being more efficient than pure live wire and snake methods.