Propylene polymers having a melt flow index in the range from 3.0 dg/min to 8.0 dg/min can be particularly suited for high-tenacity fibers and yarns and nonwovens. The propylene polymers can be produced by a process that includes polymerizing propylene or propylene and at least one comonomer in presence of a Ziegler-Natta polymerization catalyst, an aluminium alkyl, and hydrogen.