The reaction C(P-3(J)) + C2D2(X(1)Sigma (+)(g)) -> C3D + D(S-2(1/2)) has been studied with pulsed, crossed, supersonic molecular beams, in the range of relative translational energies epsilon (tr) = 4-240 meV. The D(S-2(1/2)) product has been detected by laser-induced fluorescence. The reaction is found to be slightly exoergic, with no barrier. Relative integral cross-sections are proportional to (epsilon (tr))(-0.72+/-0.03) below epsilon (tr) = 50 meV. These findings, along with energetics considerations, suggest that the analogous C(P-3(J)) + C2H2(X(1)Sigma (+)(g)) -> C3H + H(S-2(1/2)) reaction is also a barrierless process.