Polymers of propene are prepared by means of a Ziegler-Natta catalyst system composed of (1) a titanium component based on a finely divided shape-dictating silica gel and containing titanium, magnesium, chlorine and a benzenecarboxylic acid derivative, (2) an aluminum component and (3) a silane component, the titanium component (1) being obtained by (1.1) first preparing (I) a carrier material from (Ia) a silica gel, (Ib) an organomagnesium compound (Ic) a gaseous chlorinating agent and (Id) a specific phthalic acid derivative by (1.1.1) first reacting (Ia) with (Ib), then (1.1.2) passing (Ic) into the product of (1.1.1) together with the phthalic acid derivative (Id) and isolating (I), (1.2) preparing a solid-phase intermediate from (I), (II) an alkanol and (III) titanium tetrachloride by (1.2.1) first reacting (I) with (II), then (1.2.2) introducing (III) into the product resulting from (1.2.1), then (1.3) extracting the solid-phase result from (1.2) with titanium tetrachloride or a titanium tetrachloride/ethylbenzene mixture, and finally (1.4) washing the solid-phase result from (1.3) with a liquid hydrocarbon.