The electronic structure of the K-2 molecule is revisited to describe the 36 highly excited states dissociating into the three limits K(4s) + K(4f), K(4s) + K(6p), and K(4s) + K(5d), which have not yet been investigated theoretically. Potential energy curves and spectroscopic constants are (re)displayed for the 98(1,3) Lambda(g,u)((+,-)) molecular states correlated adiabatically to the limits up to K(4s) + K(5d). For the 10 states dissociating adiabatically into K(4p) + K(4p) and limits above for which experimental data are available, averaged errors of present results are found to be DeltaR(e) = 0.07a(0), DeltaT(e) = 50 cm(-1), Deltaomega(e) = 0.8 cm(-1). and DeltaD(e) = 60 cm(-1). Full energy data are available at the following address http://lasim.univ-lyon1.fr/allouche/k2.html (C) 2004 American Institute of Physics.