A method of fabricating a textile structure of varying thickness including using a loom to weave a fiber texture in the form of a strip extending lengthwise along a longitudinal axis and widthwise along an axis perpendicular to the longitudinal axis, and causing the texture to be wound under tension onto a mandrel. The texture includes a portion presenting extra thickness. During the winding of the texture, a spacer element is interposed between adjacent turns of the fiber texture onto the mandrel. Each spacer element extends in the width direction of the texture over a portion thereof situated outside the portion of extra thickness and presenting, over the portion of the texture situated outside the portion of extra thickness, a thickness that corresponds at least to the difference between thicknesses of the portion of extra thickness and of the portion of the texture situated outside the portion of extra thickness.