The predissociation mechanism of D near the threshold for the production of the D(2s, 2p) fragments has been studied by measuring the fragment yield spectra, fragment velocity map images, and fragment branching ratios D(2s)/(D(2s) + D(2p)) using a combination of XUV laser and velocity map imaging. The predissociation dynamics of the 2pπCΠ(υ = 19) and 3pπDΠ(υ = 4,5) states were studied. The 2pπCΠ(υ = 19) state is a bound state due to a shallow barrier. For the R(0) transition to the 2pπCΠ(υ = 19) state, the experimental results suggest that the predissociation occurs via three channels with decreasing importance: l-uncoupling with the 2pσBΣ state, tunneling, and l-uncoupling with the 3pσB'Σ state. For the R(1) transition to the 2pπCΠ(υ = 19) state, the first channel plays the dominant role. For the Q(1) transition to the 2pπCΠ(υ = 19) state, the predissociation occurs via tunneling as required by symmetry. For the predissociation of the 3pπDΠ(υ = 4,5) states, the experimental data confirm the earlier results indicating that the main perturbing state is 3pσB'Σ. The Beutler-Fano profiles and the associated spectroscopic parameters for the various predissociations have also been obtained. The measured Fano-parameters q for the P- and R-branches of the 3pπDΠ state are found to have opposite signs, and their relationships are in agreement with a formula derived from the Fano equation. Rotationally resolved Beutler-Fano profiles were measured for the P(2) and P(3) lines.