New experimental data on the pd -> 3He pi+ pi- reaction obtained with the COSY-MOMO detector below the three-pion threshold are presented. The reaction was also studied in inverse kinematics with a deuteron beam and the higher counting rates achieved were especially important at low excess energies. The comparison of these data with inclusive pd -> 3He+X rates allowed estimates also to be made of pi0 pi0 production. The results confirm our earlier findings that close to threshold there is no enhancement at low excitation energies in the pi+ pi- system, where the data seem largely suppressed compared to phase space. Possible explanations for this behavior, such as strong p- waves in the pi+pi- -system or the influence of two-step processes, are explored.