The bimolecular gas-phase reaction between suprathermal atomic deuterium atoms and jetcooled deuterium iodide, (\mathrm{D}+\mathrm{DI} \rightarrow \mathrm{D}{2}+\mathrm{I}), was used to generate a wide range of rovibrationally excited deuterium molecules, (D{2}). Using ((2+1)) resonance-enhanced multiphoton ionization spectroscopy, we measured many previously unreported (E, F^{\prime} \Sigma_{g}^{+}\left(v_{E}^{\prime}=0\right.) and (\left.\mathrm{I}, J^{\prime}=J^{\prime \prime}\right)-X) (' \Sigma_{\delta}^{+}\left(v^{\prime \prime}=0-5, J^{\prime \prime}\right)) two-photon transition energies, for rotational levels that range from (J^{\prime \prime}=0) to 26. Experimental observation of many transitions corresponding to high rotational levels allowed the testing of higher-order molecular constants for the (X^{\prime} \Sigma_{\varepsilon}^{+})ground state as well as for the (E, F) ({ }^{\prime} \Sigma_{\varepsilon}^{+})excited electronic state. Significant discrepancies were found between observed transition energies and those calculated from known molecular constants (i.e., more than a few hundred (\mathrm{cm}^{-1}) ) for the higher rotational levels. Separately, rovibrational term values of the (X^{1} \Sigma_{g}^{+})ground state and (E, F^{1} \Sigma_{g}^{+})state were calculated, using ab initio methods, to provide calculated transition energies. Excellent agreement is observed between the experimental and ab initio calculated transition energies, which confirms the accuracy of the theoretical potentials. 1995 Academic Pres, Inc