Iron-sulfur clusters with [3Fe-4S] cores are widely distributed in biological systems. In the oxidized state, designated [3Fe-4S]+, these electron-transfer agents have an electronic ground state with S = 1/2 , and they exhibit EPR signals centered at g = 2.01. It has been established by Mossbauer spectroscopy that the three iron sites of the cluster are high-spin Fe3+, and the general properties of the S = 1/2 ground state have been described with the exchange Hamiltonian H(exch) = J12S1·S2 + J23S2·S3 + J13S1·S3. Some [3Fe-4S]+ clusters (type 1) have their g-values confined to the range between g = 2.03 and 2.00 while others (type 2) exhibit a continuous distribution of g-values down to g ≃ 1.85. Despite considerable efforts in various laboratories no model has emerged that explains the g-values of type 2 clusters. The 4.2 K spectra of all [3Fe-4S]+ clusters have broad features which have been simulated in the past by using 57Fe magnetic hyperfine tensors war anisotropies that are unusually large for high-spin ferric sites. It is proposed here that antisymmetric exchange, H(AS) = d·(S1 x S2 + S2 x S3 + S3 x S1), is the cause of the g-value shifts in type 2 clusters. We have been able to fit the EPR and Mossbauer spectra of the 3Fe clusters of beef heart aconitase and Desulfovibrio gigas ferredoxin II by using antisymmetric exchange in combination with distributed exchange coupling constants J12, J13, and J23 (J-strain). While antisymmetric exchange is negligible for aconitase (which has a type 1 cluster), fits of the ferredoxin II spectra require |d| ≃ 0.4 cm-1. Our studies show that the data of both proteins can be fit using the same isotropic 57Fe magnetic hyperfine coupling constant for the three cluster sites, namely a = -18.0 MHz for aconitase and a = -18.5 MHz for the D. gigas ferredoxin. The effects of antisymmetric exchange and J-strain on the Mossbauer and EPR spectra are discussed.