A brush assembly with an applicator rod, a brush sleeve with a tubular core member and a plurality of bristles, a rod hole in the distal end of the applicator rod, and a rivet for being received into the rod hole to retain the brush sleeve. A peripheral retaining wall can retain and protect a proximal end of the brush sleeve. The brush sleeve can have radially projecting, diamond-shaped bristles and can be slidably received over a body portion of the rivet or over a support stem forming a distal portion of the applicator rod. The body portion of the rivet or the support stem can have a non-circular cross section or an arcuate longitudinal profile to induce the brush sleeve to have the non-circular cross section or acruate longitudinal profile. A method for producing brush assemblies can produce brush assemblies with brush sleeves of varied cross sections.