In this paper we study special Moufang sets MðU; tÞ, with U abelian, under the additional restriction that they have finite Morley rank. Our result states that the little projective group of such a Moufang set must be isomorphic to PSL 2 ðKÞ for an algebraically closed field K provided that U has characteristic 2 and that infinitely many endomorphisms of U centralize the Hua subgroup. This complements a result of De Medts and Tent that addresses the odd characteristic case.