An optimal set of 1050 rovibronic energy levels for 35 triplet electronic states of D₂ has been obtained by means of a statistical analysis of all available wavenumbers of triplet-triplet rovibronic transitions studied in emission, absorption, laser and anticrossing spectroscopic experiments of various authors. We used a new method of analysis (Lavrov and Ryazanov 2005 JETP Lett. 81 371-4), which does not need any a priori assumptions concerning the molecular structure, being based on only two fundamental principles: Rydberg-Ritz and maximum likelihood. The method provides the opportunity to obtain the root-mean-square estimates for uncertainties of the experimental wavenumbers independent from those presented in the original papers. A total of 234 from 3822 published wavenumber values were found to be spurious, while the remaining set of the data may be divided into 20 subsets (samples) of uniformly precise data having close to normal distributions of random errors within the samples. New experimental wavenumber values of 125 questionable lines were obtained in the present work. Optimal values of the rovibronic levels were obtained from the experimental data set consisting of 3713 wavenumber values (3588 old and 125 new). The unknown shift between levels of ortho- and para-deuterium was found by least-squares analysis of the a³Σ ⁺_g, v = 0, N = 0 18 rovibronic levels with odd and even values of N. All the energy levels were obtained relative to the lowest vibro-rotational level (v = 0, N = 0) of the a³Σ ⁺_g electronic state, and presented in tabular form together with the standard deviations of the empirical determination. New energy-level values differ significantly from those available in the literature.