The present disclosure describes bottle closure assemblies which are made at least in part with a polyethylene copolymer having good organoleptic properties. The bottle closure assembly includes a cap portion, an elongated tether portion, and a retaining means portion. The retaining means portions engages a bottle neck or an upper portion of a bottle. The elongated tether portion connects at least one point on the cap portion to at least one point on the retaining means portion so as to prevent loss of the cap portion from a bottle.