A fitting for the mutual joining of a threaded terminal element and a smooth surface pipe having one end, comprising: - a tubular core defining an axis having a front portion which can be coupled or monolithic with the threaded terminal element and a rear portion which can be inserted into the end of the pipe to come into contact with the internal surface thereof; - a ring nut which can be mutually screwed on said threaded terminal element having an outer surface designed to be gripped by a user and an inner surface designed to be faced toward the pipe, said inner surface including a first annular seat with a first threaded portion which can be coupled to the threaded terminal element, a second opposite substantially frustoconical portion and a third portion interposed therebetween defining a first groove with a surface perpendicular to said axis, the latter and said second portion defining a step; - an elastic sleeve which can be fitted on the pipe having an inner surface designed to come into contact with the outer surface of the pipe with a second substantially continuous annular seat having a first predefined diameter (Ø1), an outer surface with a third portion facing said second portion of said ring nut and a fourth substantially frustoconical portion mutually consecutive to the first, a front surface facing said threaded terminal element and at least one plastically deformable area with a second groove parallel to said axis; - an elastomeric gasket arranged peripherally with respect to said tubular core and designed to remain interposed between the end of the pipe, said sleeve and the threaded terminal element to provide the local hydraulic sealing; wherein upon reciprocal screwing said ring nut and said threaded terminal element, said step is designed to mutually impact said fourth portion of said sleeve in a single point of tangency, the screwing causing the axial translation of said sleeve and an ensuing radial compression thereof so that: the end of the pipe is axially compressed against said elastomeric gasket so as to provide the aforementioned hydraulic sealing; and - said second annular seat is progressively radially compressed along said axis so as to radially compress the end of the pipe against said elastomeric gasket so as to obtain a first mechanical sealing, the second annular seat having - after screwing - a second predetermined diameter (Ø2) at said front surface that is substantially smaller than said diameter ( Ø1), said plastically deformable area collapsing so that said inner surface remains substantially continuous and free of recesses. - a tubular core defining an axis having a front portion which can be coupled or monolithic with the threaded terminal element and a rear portion which can be inserted into the end of the pipe to come into contact with the internal surface thereof; - a ring nut which can be mutually screwed on said threaded terminal element having an outer surface designed to be gripped by a user and an inner surface designed to be faced toward the pipe, said inner surface including a first annular seat with a first threaded portion which can be coupled to the threaded terminal element, a second opposite substantially frustoconical portion and a third portion interposed therebetween defining a first groove with a surface perpendicular to said axis, the latter and said second portion defining a step; - an elastic sleeve which can be fitted on the pipe having an inner surface designed to come into contact with the outer surface of the pipe with a second substantially continuous annular seat having a first predefined diameter (Ø1), an outer surface with a third portion facing said second portion of said ring nut and a fourth substantially frustoconical portion mutually consecutive to the first, a front surface facing said threaded terminal element and at least one plastically deformable area with a second groove parallel to said axis; - an elastomeric gasket arranged peripherally with respect to said tubular core and designed to remain interposed between the end of the pipe, said sleeve and the threaded terminal element to provide the local hydraulic sealing; - said second annular seat is progressively radially compressed along said axis so as to radially compress the end of the pipe against said elastomeric gasket so as to obtain a first mechanical sealing, the second annular seat having - after screwing - a second predetermined diameter (Ø2) at said front surface that is substantially smaller than said diameter ( Ø1), said plastically deformable area collapsing so that said inner surface remains substantially continuous and free of recesses.