Three new heterometallic complexes with formulas of [(Dy2Co2III)-Co-III(OMe)(2)(teaH)(2)(acac)(4)(NO3)(2)] (1), [(Dy2Co2III)-Co-III(OH)(2)-(teaH)(2)(acac)(4)(NO3)(2)]center dot 4H(2)O (2), and [(Dy2Co2III)-Co-III(OMe)(2)(mdea)(2)-(acac)(4)(NO3)(2)] (3) were characterized by single-crystal X-ray diffraction and by dc and ac magnetic susceptibility measurements. All three complexes have an identical "butterfly"-type metallic core that consists of two Dy-III ions occupying the "body" position and two diamagnetic low-spin Co-III ions occupying the outer "wing-tips". Each complex displays single-molecule magnet (SMM) behavior in zero applied magnetic field, with thermally activated anisotropy barriers of 27, 28, and 38 K above 7.5 K for 1-3, respectively, as well as observing a temperature-independent mechanism of relaxation below 5 K for 1 and 2 and at 3 K for 3, indicating fast quantum tunneling of magnetization (QTM). A second, faster thermally activated relaxation mechanism may also be active under a zero applied dc field as derived from the Cole-Cole data. Interestingly, these complexes demonstrate further relaxation modes that are strongly dependent upon the application of a static dc magnetic field. Dilution experiments that were performed on 1, in the {(Y2Co2III)-Co-III} diamagnetic analog, show that the slow magnetic relaxation is of a single-ion origin, but it was found that the neighboring ion also plays an important role in the overall relaxation dynamics.