An extension to connected operator filtering is proposed here for 3D still images (e.g. biomedical volumes). The "surface preservation" property of this kind of morphological processing can be exploited to obtain a "simplification" effect on the data, deriving from the cancellation of some undesired 3D structures; this is achieved by some filtering criteria which can be related to different objectives, varying from denoising to real structure removal purposes. We also show how the simplification process constitutes a useful pre-processing step to improve the performance of an automatic and/or assisted morphological segmentation of volumetric objects in the case of noisy, natural and complex data, such as MR and CT volumes.