Threaded tubular connection for the drilling and/or exploitation of hydrocarbon wells, comprising a first tube equipped at a first distal end with a male tool joint and a second tube equipped at a second distal end with a female tool joint, the male tool joint being capable of being assembled by makeup with the female tool joint, the first tube assembled to the second tube together defining a longitudinal axis, the male tool joint comprising, in this order from a free edge of the first distal end towards a body of this first tube: a male inner sealing surface, a first male threaded portion, a male abutment shoulder, a male intermediate sealing surface, and a second male threaded portion, the female tool joint comprising a female inner sealing surface intended to form an inner seal by radial interference with the first male sealing surface, a first female threaded portion engaged with the first male threaded portion, a female abutment shoulder in abutting contact with the male abutment shoulder, a female intermediate sealing surface intended to form an intermediate seal by radial interference with the male intermediate sealing surface, and a second female threaded portion engaged with the second male threaded portion, when the connection is assembled, the free edge of the first distal end being at a non-zero axial distance (d) from the female tool joint in the assembled position, the male threaded portions each comprising at least one helix equipped with a load flank, a thread crest, a stabbing flank, a thread root, such that a pitch of the load flank LFLp 1 and a pitch of the stabbing flank SFLp1 of the first male threaded portion, and respectively a pitch of the load flank LFLp2 and a pitch of the stabbing flank SFLp2 of the second male threaded portion fulfil the following condition: SFL p 1 = LFL p 1 = SFL p 2 = LFL p 2 = k 1 where k1 is a constant for at least two complete turns of each of the helices, and characterised in that the first threaded portion of the female tool joint comprises an annular groove to receive excess grease. the male tool joint comprising, in this order from a free edge of the first distal end towards a body of this first tube: a male inner sealing surface, a first male threaded portion, a male abutment shoulder, a male intermediate sealing surface, and a second male threaded portion, the female tool joint comprising a female inner sealing surface intended to form an inner seal by radial interference with the first male sealing surface, a first female threaded portion engaged with the first male threaded portion, a female abutment shoulder in abutting contact with the male abutment shoulder, a female intermediate sealing surface intended to form an intermediate seal by radial interference with the male intermediate sealing surface, and a second female threaded portion engaged with the second male threaded portion, when the connection is assembled, the free edge of the first distal end being at a non-zero axial distance (d) from the female tool joint in the assembled position, the male threaded portions each comprising at least one helix equipped with a load flank, a thread crest, a stabbing flank, a thread root, such that a pitch of the load flank LFLp 1 and a pitch of the stabbing flank SFLp1 of the first male threaded portion, and respectively a pitch of the load flank LFLp2 and a pitch of the stabbing flank SFLp2 of the second male threaded portion fulfil the following condition: SFL p 1 = LFL p 1 = SFL p 2 = LFL p 2 = k 1 where k1 is a constant for at least two complete turns of each of the helices, and characterised in that the first threaded portion of the female tool joint comprises an annular groove to receive excess grease.