A method is for plugging a well wherein the well, at least along a longitudinal section to be plugged, is provided with one or more pipe bodies forming a radial boundary between the well and a surrounding formation. The method includes (D), lowering a flow-through string into the well and, by the flow-through string, supplying a fluidized plugging material along the longitudinal section in the well, and at least within the innermost of said one or more pipe bodies in the well. The method, before step (D), also comprises (A), lowering one or more explosive charges into the well and onto the longitudinal section to be plugged, and detonating one or more of said explosive charges so as to extend the diameter of one or more of said pipe bodies at one or more places along the longitudinal section to be plugged. A system is for plugging a well.