The two infrared-active vibrational bands of the 3 ν 3 manifold of SF 6 have been recorded at T = 160 K with near Doppler-limited resolution using a tunable laser difference-frequency spectrometer. Most of the principal structure has been identified, and over 700 lines with J ≤ 33 have been fitted with a model Hamiltonian which allows the l = 1 and l = 3 subbands to interact. The analysis yields the values of ten spectroscopic constants. When earlier results for the ν 3 band are considered, the values of eight additional constants are derived. The effective harmonic frequency, ω 3 0, and the three anharmonic coefficients X 33, G 33, and T 33, have been determined with high precision, so that the vibrational levels in the nν 3 ladder can be predicted accurately for several values of n. The Cartesian basis ( n 3 x , n 3 y , n 3 z ) is found to be the best representation for the vibrational sublevels. Analysis of the rovibrational line strengths reveals that the weak (2, 1, 0) band of 3 ν 3 has a very small intrinsic dipole transition moment, so that this band derives most of its intensity by “borrowing” from the strong (3, 0, 0) band.