The cellulose product comprises at least a first ply of embossed cellulose material and a second ply of embossed cellulose material, glued together. The first ply comprises: a first series of embossing protuberances with a first height (H′1) and a top surface to which a glue is applied which bonds the first ply and the second ply to one another; a second series of micro-embossing protuberances with a second height (H′2) lower than the first height (H′1); a third series of micro-embossing protuberances with a third height (H′3) lower than the second height (H′2). The protuberances of the first series are distributed over areas of the first ply, where the micro-embossing protuberances of the second series and the micro-embossing protuberances of the third series are absent.