We present the results from analyses of Suzaku observations of the supergiant X-ray binaries IGR J16207-5129 and IGR J17391-3021. For IGR J16207-5129, we provide the first broadband (0.5--60 keV) spectrum from which we confirm a large intrinsic column density (nH = 16e22 /cm2), and constrain the cutoff energy for the first time (Ec = 19 keV). We observed a prolonged (> 30 ks) attenuation of the X-ray flux which we tentatively attribute to an eclipse of the probable neutron star by its massive companion. For IGR J17391-3021, we witnessed a transition from quiescence to a low-activity phase punctuated by weak flares whose peak luminosities in the 0.5--10 keV band are only a factor of 5 times that of the pre-flare emission. The weak flaring is accompanied by an increase in the absorbing column which suggests the accretion of obscuring clumps of wind. Placing this observation in the context of the recent Swift monitoring campaign, we now recognize that these low-activity epochs constitute the most common emission phase for this system, and perhaps in other SFXTs as well.