We present a set of interactive, free-form editing operators for direct manipulation of level-set models that supports the creation and removal of surface detail. The mathematics, data structures and algorithms needed to implement numerous level-set modeling capabilities have been developed. The first component of these capabilities identifies the Region-of-Influence (ROI) on the surface to be modified, and the specification of user handles, i.e. a point or a curve within the ROI, that are used to control the free- form surface edits. The editing operators include pulling the level-set surface by a handle with the surface changes occurring symmetrically around the handle or within the ROI, surface offsetting and carving, deformations towards a profile curve and localized smoothing. The editing operators are implemented with specialized speed functions, which are incorporated into the level set partial differential equation (PDE). The PDE is then evolved to produce the desired model modification. The specific form of each speed function is described in detail. The operators have been combined with an OpenGL interface and the VISPACK level-set library to create a preliminary interactive level-set modeling system. VISPACKÔ's narrow-band data structures have been extended to localize all computations and updates to optimize running time and provide interactive performance. Additional sketch-based level-set editing operators have been implemented within the system, and are described elsewhere. A variety of level-set models are presented to demonstrate the effectiveness of the editing operators.