A preform (3; 30), in particular for a stiffener, with a three-dimensional fibrous structure having a thickness and being woven in a single piece by multilayer weaving of layers of warp yarns (17; 170) and layers of weft yarns (19; 190) distributed along the thickness, the preform defining at least one first portion (21; 210) and at least one second portion (23; 230) extending the first portion toward a thin edge (7; 70) of the preform, the preform comprising: - a first group (C1; C10A, C10B) of successive layers of warp yarns, which includes at least one layer of warp yarns and which is external in the first portion, - a second group (C2; C20A, C20B) of successive layers of warp yarns, which includes at least one layer of warp yarns and which is located immediately below the first group of layers of warp yarns, - a first group (T1; T10A, T10B) of successive layers of weft yarns, which includes at least one layer of weft yarns and which is connected according to a weave with the first group of layers of warp yarns, so as to be external in the first portion, and - a second group (T2; T20A, T20B) of successive layers of weft yarns, which includes at least one layer of weft yarns and which is located immediately below the first group (T1; T10A, T10B) of layers of weft yarns in the first portion (21; 210), the second group of layers of weft yarns being absent from the second portion (23; 230), while: - the number of layers of warp yarns (17; 170) forming the second portion (23; 230) is smaller relative to the number of layers of warp yarns forming the first portion (21; 210), due to the absence of the first group (C1; C10A, C10B) of layers of warp yarns in the second portion, such that the second portion has a smaller thickness relative to that of the first portion and such that the second group (C2; C20A, C20B) of layers of warp yarns is external in the second portion, and - the first group (T1; T10A, T10B) of layers of weft yarns (19; 190) extends into the second portion, while being connected according to a weave with the second group of layers of warp yarns in the second portion, such that the first group of layers of weft yarns is also external in the second portion; characterized in that: - the weft yarns (19; 190) of the first group (T1; T10A, T10B) of layers of weft yarns have a yarn size smaller than the yarn size of the weft yarns of the second group (T2; T20A, T20B) of layers of weft yarns; and/or - the warp yarns (17; 170) of the first group (C1; C10A, C10B) of layers of warp yarns have a yarn size smaller than the yarn size of the warp yarns of the second group (C2; C20A, C20B) of layers of warp yarns. - a first group (C1; C10A, C10B) of successive layers of warp yarns, which includes at least one layer of warp yarns and which is external in the first portion, - a second group (C2; C20A, C20B) of successive layers of warp yarns, which includes at least one layer of warp yarns and which is located immediately below the first group of layers of warp yarns, - a first group (T1; T10A, T10B) of successive layers of weft yarns, which includes at least one layer of weft yarns and which is connected according to a weave with the first group of layers of warp yarns, so as to be external in the first portion, and - a second group (T2; T20A, T20B) of successive layers of weft yarns, which includes at least one layer of weft yarns and which is located immediately below the first group (T1; T10A, T10B) of layers of weft yarns in the first portion (21; 210), the second group of layers of weft yarns being absent from the second portion (23; 230), - the number of layers of warp yarns (17; 170) forming the second portion (23; 230) is smaller relative to the number of layers of warp yarns forming the first portion (21; 210), due to the absence of the first group (C1; C10A, C10B) of layers of warp yarns in the second portion, such that the second portion has a smaller thickness relative to that of the first portion and such that the second group (C2; C20A, C20B) of layers of warp yarns is external in the second portion, and - the first group (T1; T10A, T10B) of layers of weft yarns (19; 190) extends into the second portion, while being connected according to a weave with the second group of layers of warp yarns in the second portion, such that the first group of layers of weft yarns is also external in the second portion; - the weft yarns (19; 190) of the first group (T1; T10A, T10B) of layers of weft yarns have a yarn size smaller than the yarn size of the weft yarns of the second group (T2; T20A, T20B) of layers of weft yarns; and/or - the warp yarns (17; 170) of the first group (C1; C10A, C10B) of layers of warp yarns have a yarn size smaller than the yarn size of the warp yarns of the second group (C2; C20A, C20B) of layers of warp yarns.