It is well known that magnetic susceptibility variations lead to signal voids in MRI. However, recent work has shown that positive-contrast imaging of susceptibility-induced field variations can provide signal enhancements rather than signal losses. In this paper, we propose a new method for generating positive contrast from off-resonant spins with steady-state free precession (SSFP) magnetic resonance imaging. Based on theory and experiments, we demonstrate that positive-contrast images can be acquired in the presence of susceptibility-shift media with low flip angle excitations that are determined by the spin relaxation time constants of the imaging medium. Compared to other techniques, this technique is substantially faster and has low specific absorption rates, permitting high-field imaging. In addition to acquiring positive-contrast images, we also show that it is possible to suppress the imaging medium to desired levels; thereby allowing for simultaneous registration of the background details surrounding the susceptibility-shift media. Among practical applications, we anticipate that the proposed technique can potentially facilitate high field magnetic-resonance-based molecular imaging.