We discuss building models for nucleon generalized parton distributions H and E that are based on the formalism of double distributions (DDs). We found that the usual "DD + D-term'' construction should be amended by an extra term, xi E-+(1)(x, xi) built from the alpha/beta moment of the DD ed e(beta,alpha) that generates generalized parton distribution E(x, xi). Unlike the D term, this function has support in the whole -1 <= x <= 1 region, and in general does not vanish at the border points broken vertical bar x broken vertical bar = xi.