The search for "higher homotopy Hopf algebras" (known today as A_\infty-bialgebras) was initiated by this author in a talk at Jim Stasheff's 1996 schriftfest. The idea in that talk was to think of a DG bialgebra as some (unknown) higher homotopy structure with trivial higher order structure and apply a graded version of Gerstenhaber and Schack's bialgebra deformation theory. In certain cases, the H-bi(co)module structure encoded in the differential detects the higher order structure relations in the deformation. This motivates the notion of an A_\infty-bialgebra given by S. Saneblidze and this author in 2004, and in light of this, we prove that a deformation of a DG bialgebra as an A_\infty-bialgebra admits at most one non-vanishing higher order operation.