  We discuss building models for nucleon generalized parton distributions
(GPDs) 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 e(\beta,\alpha) that generates GPD E(x,\xi). Unlike the D-term, this
function has support in the whole -1 \leq x \leq 1 region, and in general does
not vanish at the border points |x|=\xi.
