@It'saboutEnglish Yes, I might use pieces, but I would prefer section or portion, or maybe strand--though again, there's an issue with strand in that it often refers to just a single hair. All of these are really context dependent.
@It'saboutEnglish Well, like I said, "section off a section" is awkward because of the duplication, but "Section off a small portion" would be perfectly fine to my ear