A nonwoven web that contains a plurality of fibers formed from a polyolefin composition is provided. The polyolefin composition contains a rigid propylene polymer that has a relatively high melting temperature and modulus of elasticity, which can provide good strength and durability to the nonwoven web. The polyolefin composition also contains a ductile propylene polymer that has a relatively high melt flow index, which can help achieve relatively fine fibers that minimize the stiffness of the web. In addition to a rigid and ductile polymer, the polyolefin composition also contains a slip additive (e.g., fatty acid derivative). Among other things, such an additive can even further enhance the overall softness of the composition.