In this paper, the authors continue their investigation of loops which give rise to alternative loop rings. If the coefficient ring has characteristic 2, these loops turn out to form a surprisingly wide class, in contrast to the situation of characteristic ≠ 2. This paper describes many properties of this class, includes diverse examples of Moufang loops which are united by the fact that they have loop rings which are alternative, and discusses analogues in loop theory of a number of important group theoretic constructions.