High-resolution laser absorption spectroscopy using concentration modulation has been applied to record the near-infrared spectrum of C-2 in an AC hollow cathode discharge of acetylene/helium mixtures. The (2,1) and (1,0) vibronic bands of the d(3)Pi(g) - c(3)E(u)(+) system have been observed in the spectral region between 12 010 and 12 540 cm(-1). While the analysis of the (1,0) band was straightforward, the (2,1) band was found to be perturbed. Using the effective Hamiltonians for (3)Pi and (3)Sigma(+) states, molecular constants for the vibrational levels of the c(3)E(u)(+) state were retrieved in least-squares fits of the observed spectral lines. The experimental conditions, detailed analysis of the perturbations, and the determined molecular constants are reported.