A new approach stemming from the adiabatic-connection (AC) formalism is proposed to derive parameter-free double-hybrid (DH) exchange-correlation functionals. It is based on a quadratic form that models the integrand of the coupling parameter, whose components are chosen to satisfy several well-known limiting conditions. Its integration leads to DHs containing a single parameter controlling the amount of exact exchange, which is determined by requiring it to depend on the weight of the MP2 correlation contribution. Two new parameter-free DHs functionals are derived in this way, by incorporating the non-empirical PBE and TPSS functionals in the underlying expression. Their extensive testing using the GMTKN30 benchmark indicates that they are in competition with state-of-the-art DHs, yet providing much better self-interaction errors and opening a new avenue towards the design of accurate double-hybrid exchange-correlation functionals departing from the AC integrand. (C) 2014 AIP Publishing LLC.