A quick coupling for the detachable connection of two pipes (C1, C2) through which a pressurized fluid flows, made up of a male element and a female element able to receive the male element by fitting along a longitudinal axis (X-X') between an uncoupled configuration and a coupled configuration of the coupling, the male element comprising: - a cylindrical male body, defining a longitudinal cavity and a distal mouth, the diameter of which is smaller than that of the cavity, - a valve movable axially inside the cavity, between a forward position in which the valve closes off the mouth and a withdrawn position in which the valve does not close off the mouth, and - a first sealing gasket that is borne by the male body or the valve, and which bears respectively on the valve or on an inner cylindrical wall (S102i) of the male body, and the female coupling element comprising: - a cylindrical female body, defining a longitudinal cavity and a distal mouth, the diameter of which is smaller than or equal to that of the cavity, - a push-piece, and - a slide valve, which is arranged radially between the female body and the push-piece and which is movable axially inside the longitudinal cavity between a forward position, in which the slide valve closes off the mouth, and a withdrawn position, in which the slide valve does not close off the mouth, and - a second sealing gasket that is borne by the slide valve or the push-piece, and which bears respectively on an outer cylindrical wall (S208e) of the push-piece or on the slide valve, wherein: - the male body or the push-piece delimits a fluid passage channel (102.1; 208.1) connecting the inside of the cavity to the distal mouth, respectively of the male element or the female element, - the passage channel (102.1; 208.1), emerging inside the cavity of the male element or the female element, fits inside a circle (C102.1; C208.1), the diameter (ø; ø') of which is respectively larger or smaller than that (D110; D210) of the first and second sealing gaskets (110, 210), - the channel (102.1; 208.1) extends between two planes that are perpendicular to the longitudinal axis, respectively between a proximal plane and distal plane, which are offset relative to one another along the longitudinal axis, characterized in that: - the channel (102.1; 208.1) is a slot along the outer cylindrical wall (S208e) of the push-piece or along the inner cylindrical wall (S102i) of the male body. - a cylindrical male body, defining a longitudinal cavity and a distal mouth, the diameter of which is smaller than that of the cavity, - a valve movable axially inside the cavity, between a forward position in which the valve closes off the mouth and a withdrawn position in which the valve does not close off the mouth, and - a first sealing gasket that is borne by the male body or the valve, and which bears respectively on the valve or on an inner cylindrical wall (S102i) of the male body, - a cylindrical female body, defining a longitudinal cavity and a distal mouth, the diameter of which is smaller than or equal to that of the cavity, - a push-piece, and - a slide valve, which is arranged radially between the female body and the push-piece and which is movable axially inside the longitudinal cavity between a forward position, in which the slide valve closes off the mouth, and a withdrawn position, in which the slide valve does not close off the mouth, and - a second sealing gasket that is borne by the slide valve or the push-piece, and which bears respectively on an outer cylindrical wall (S208e) of the push-piece or on the slide valve, - the male body or the push-piece delimits a fluid passage channel (102.1; 208.1) connecting the inside of the cavity to the distal mouth, respectively of the male element or the female element, - the passage channel (102.1; 208.1), emerging inside the cavity of the male element or the female element, fits inside a circle (C102.1; C208.1), the diameter (ø; ø') of which is respectively larger or smaller than that (D110; D210) of the first and second sealing gaskets (110, 210), - the channel (102.1; 208.1) extends between two planes that are perpendicular to the longitudinal axis, respectively between a proximal plane and distal plane, which are offset relative to one another along the longitudinal axis, - the channel (102.1; 208.1) is a slot along the outer cylindrical wall (S208e) of the push-piece or along the inner cylindrical wall (S102i) of the male body.