The known and new heterogeneous spectral data on the triplet states a ³∑ _u ⁺ , 2³Π_g, 2³∑ _g ⁺ , 3³Π_g, and 4³∑ _g ⁺ of the K₂ dimer are simultaneously fitted. The data published in J. Mol. Spectrosc. 234, 41 (2005) are refined. The new information used in the analysis contains the data on the 2³∑ _g ⁺ state, which have not been considered previously. The range of internuclear distances where the potential function of the lowest triplet state a ³∑ _u ⁺ is defined is extended.