The pionic decay rates of the excited L = 0, 1 D mesons are calculated with a Hamiltonian model within the framework of the covariant Blankenbecler-Sugar equation. The interaction between the light quark and charm antiquark is described by a linear scalar confining and a screened one-gluon exchange interaction. The decay widths of the D * mesons obtain a contribution from the exchange current that is associated with the linear scalar confining interaction. If this contribution is taken into account along with the single-quark approximation, the calculated decay rates of the charged D * mesons are readily below the current empirical upper limits if the axial coupling constant of the light constituent quarks is taken to be g q A = 0.87, but reach the empirical upper limits if g q A = 1. With the conventional values for g q A , the calculated widths of the D 1 and D * 2 mesons fall somewhat below the experimental lower limits, leaving room for other decay modes as well, such as ππ decay. The unrealistically large contribution from the axial charge operator to the calculated pion decay width of the D 1 meson is suppressed by taking into account the exchange charge effects that are associated with the scalar linear confining and vector one-gluon exchange interactions. The predicted values for the pionic widths of the hitherto undiscovered L = 1 D * 1 and D * 0 mesons are found to be smaller than previous estimates.