A high-resolution (1.16 A) X-ray structure of the nitrogenase molybdenum-iron (MoFe) protein revealed electron density from a single N, O, or C atom (denoted X) inside the central iron prismane ([6Fe]) of the [MoFe7S9:homocitrate] FeMo-cofactor (FeMo-co). We here extend earlier efforts to determine the identity of X through detailed tests of whether X = N or C by interlocking and mutually supportive 9 GHz electron spin echo envelope modulation (ESEEM) and 35 GHz electron-nuclear double resonance (ENDOR) measurements on 14/15N and 12/13C isotopomers of FeMo-co in three environments: (i) incorporated into the native MoFe protein environment; (ii) extracted into N-methyl formamide solution; and (iii) incorporated into the NifX protein, which acts as a chaperone during FeMo-co biosynthesis. These measurements provide powerful evidence that X not equal N/C, unless X in effect is magnetically decoupled from the S = 3/2 electron spin system of resting FeMo-co. They reveal no signals from FeMo-co in any of the three environments that can be assigned to X from either 14/15N or 13C: If X were either element, its maximum observed hyperfine coupling at all fields of measurement is estimated to be A(14/15NX) < 0.07/0.1 MHz, A(13CX) < 0.1 MHz, corresponding to intrinsic couplings of about half these values. In parallel, we have explicitly calculated the hyperfine tensors for X = 14/15N/13C/17O, nuclear quadrupole coupling constant e2qQ for X = 14N, and hyperfine constants for the Fe sites of S = 3/2 FeMo-co using density functional theory (DFT) in conjunction with the broken-symmetry (BS) approach for spin coupling. If X = C/N, then the decoupling required by experiment strongly supports the "BS7" spin coupling of the FeMo-co iron sites, in which a small X hyperfine coupling is the result of a precise balance of spin density contributions from three spin-up and three spin-down (3 upward arrow:3 downward arrow) iron atoms of the [6Fe] prismane "waist" of FeMo-co; this would rule out the "BS6" assignment (4 upward arrow:2 downward arrow for [6Fe]) suggested in earlier calculations. However, even with the BS7 scheme, the hyperfine couplings that would be observed for X near g2 are sufficiently large that they should have been detected: we suggest that the experimental results are compatible with X = N only if aiso(14/15NX) < 0.03-0.07/0.05-0.1 MHz and aiso(13CX) < 0.05-0.1 MHz, compared with calculated values of aiso(14/15NX) = 0.3/0.4 MHz and aiso(13CX) = 1 MHz. However, the DFT uncertainties are large enough that the very small hyperfine couplings required by experiment do not necessarily rule out X = N/C.