A fitting for the reciprocal connection of a threaded end member and a pipe with a smooth surface comprising: - a tubular core defining an axis having a front portion coupled to or monolithic with the threaded end member and a rear portion to be inserted within the end of the pipe to come in contact engage with the inner surface thereof; - a ring nut to be screwed on said threaded end member having an outer surface susceptible to be grasped by a user and an inner surface ( 5 1) susceptible to face the pipe, the inner surface including an annular seat; - an elastic sleeve to be fitted onto the pipe having an inner surface susceptible to come in contact engage with the outer surface of the pipe and a substantially fustoconical outer surface diverging with respect to said axis, said elastic sleeve having a discontinuity to allow the deformation thereof upon the screwing of said ring nut on the threaded end member; - an elastomeric seal encompassing said tubular core and susceptible to remain interposed between the end of the pipe, said elastic sleeve and the threaded end member to provide the local hydraulic seal; - a metal annular elastic member snap-fit into the annular seat of said ring nut; - a rigid ring presser having an outer surface susceptible to come into contact engage with said metal annular elastic member and a substantially fustoconical inner surface diverging with respect to said axis susceptible to come into contact engage with the substantially fustoconical outer surface of said sleeve; wherein the outer surface of said rigid ring presser has a step susceptible to impact against said metal annular elastic member upon the screwing of said ring nut on the threaded end member so as to promote the axial translation of said rigid ring presser and the consequent radial compression of said elastic sleeve, so as to radially compress the end of the pipe against said rear portion of said tubular core, said metal annular elastic member having a substantially circumferential section so that the contact with the step of said rigid ring presser occurs in a single tangency point, in order to avoid unwanted twisting of the pipe upon the screwing of said sleeve on the threaded end member. - a tubular core defining an axis having a front portion coupled to or monolithic with the threaded end member and a rear portion to be inserted within the end of the pipe to come in contact engage with the inner surface thereof; - a ring nut to be screwed on said threaded end member having an outer surface susceptible to be grasped by a user and an inner surface ( 5 1) susceptible to face the pipe, the inner surface including an annular seat; - an elastic sleeve to be fitted onto the pipe having an inner surface susceptible to come in contact engage with the outer surface of the pipe and a substantially fustoconical outer surface diverging with respect to said axis, said elastic sleeve having a discontinuity to allow the deformation thereof upon the screwing of said ring nut on the threaded end member; - an elastomeric seal encompassing said tubular core and susceptible to remain interposed between the end of the pipe, said elastic sleeve and the threaded end member to provide the local hydraulic seal; - a metal annular elastic member snap-fit into the annular seat of said ring nut; - a rigid ring presser having an outer surface susceptible to come into contact engage with said metal annular elastic member and a substantially fustoconical inner surface diverging with respect to said axis susceptible to come into contact engage with the substantially fustoconical outer surface of said sleeve;