Fibre preforms of varying thickness

In a portion of the preform to be made in which the preform is to be of reduced thickness by having a recess formed therein, a mask (181, 182, ...) is interposed between pairs of adjacent layers (121, 122, ...), the mask being made of a thin film of material through which the needles can pass during needling while opposing the passage of significant quantities of fiber taken by the needles, and after it has been needled, each layer is cut out around a line corresponding to the outline of the recess in the preform at the level where the layer is situated in the preform. A mask situated between two cutout layers occupies an area that is not less than the area between the cutout lines of the two layers, such that the portions of the layers (121, 122, ...) that are delimited by the cutout lines are not securely connected to the remainder of the preform by the needling, thereby enabling the recess to be formed after all the layers have been needled by withdrawing the cutout portions of the layers ...