An adhesive tape, especially for wrapping cables, consisting of a preferably textile carrier and of a pressure-sensitive adhesive which is applied on at least one side of the carrier and is in the form of a dried polymer dispersion, the polymer being synthesized from: e) 90% to 99% by weight of n-butyl acrylate and/or 2-ethylhexyl acrylate f) 0% to 10% by weight of an ethylenically unsaturated monomer having an acid or acid-anhydride function g) 10% to 1% by weight of one or more ethylenically unsaturated monofunctional monomers different from (a) and (b) h) 0% to 1% by weight of a difunctional or polyfunctional monomer and the pressure-sensitive adhesive comprising between 15 and 100 parts by weight of a tackifier (based on the mass of the dried polymer dispersion).