We use QCD sum rules to study the possible existence of QQ - (u) over bar(d) over bar mesons, assumed to be a state with J(P) = 1(+). For definiteness, we work with a current with an axial heavy diquark and a scalar light anti-diquark, at leading order in alpha(s). We consider the contributions of condensates up to dimension eight. For the b-quark, we predict M-Tbb = (10.2 +/- 0.3) GeV, which is below the (B) over bar(B) over bar* threshold. For the c-quark, we predict M-Tcc = (4.0 +/- 0.2) GeV, in agreement with quark model predictions. (c) 2007 Elsevier B.V. All rights reserved.