The ground states of BNC, BCN, and C-3 were studied using the full-valence CASSCF (complete active space SCF) and CCSD(T) (augmented coupled cluster) methods and basis sets of spdf and spdfg quality. Full quartic force fields were obtained. r(c), and stretching fundamentals for C-3 are found to be in excellent agreement with experiment; r(0) and the bending fundamental reveal shortcomings in the bending part of the potential. The BNC ground state ((1) Sigma(+)) is only slightly less strongly bound than C-3 and is 9.5+/-0.5 kcal/mol lower in energy than the ground state of BCN. No other low-lying structures or states were found. Stretching fundamentals in BNC are affected by a severe Fermi resonance. Best estimates for the molecular constants are as follows. BNC : Sigma D-0 = 300.5+/-1 kcal/mol, r(c)(CN) = 1.167 Angstrom, r(c)(NC) = 1.416 Angstrom, omega(1) = 2075 cm(-1), omega(2) = 998 cm(-1), omega(3) = 131 cm(-1), v(1) = 2076 cm(-1), v(2) = 991 cm(-1). BCN : Sigma D-0 = 291.0+/-1 kcal/mol, r(c)(CN) = 1.135 Angstrom, r(c)(BC) = 1.597 Angstrom, omega(1) = 2197 cm(-1), omega(2) = 812 cm(-1), omega(3) = 204 cm(-1), v(1) = 2166 cm(-1), v(1) = 810 cm(-1). Both stretching fundamentals are computed to have high infrared intensities for both BNC and BCN. Spectroscopic constants for isotopic forms are also given. The best computed Sigma D-0 for C-3 is 314.7+/-1 kcal/mol, in very good agreement with experiment but with a smaller uncertainty.