Precise measurements of the frequencies of a number of new rotational transitions of α 3Π CO (v = 0-4) in the range 250-500 GHz are reported. In addition earlier measurements of the J = 0-1 frequencies near 90 GHz have been repeated at higher precision and extended to include the v = 6 lines. The nonlinear least-squares analysis of this microwave data combined with the lambda doublet transition frequencies of Klemperer and co-workers was carried out for v=0-4 by direct diagonalization of a Hamiltonian matrix that included the relevant v subblock of the a 3Π state along with the subblocks for v′ = 0-10 of the a′ 3Σ+ state. The new frequencies make possible the determination from the rf-microwave data set of several parameters that previously had to be assumed, and the method of treating most of the a-a′ perturbations directly in the large matrix yields parameters, especially lambda doubling constants, which vary less, but more smoothly, with J than before. The later smoothness is found to be enhanced by inclusion of an off-diagonal, spin-spin interaction in the a-a′ perturbation Hamiltonian, as was done in published fits of FTIR spectra of the a′ 3Σ+-a 3Π system. We also discuss the theory of the perturbed Zeeman effect of a 3Π CO, along with some preliminary measurements, and report a value of the pressure broadening parameter for a typical rotational transition in this state. © 1988 American Institute of Physics.