To perform automatic, unconscious inference, the human brain must solve the binding problem by correctly grouping properties with objects. Temporal binding models like SHRUTI already suggest much of how this might be done in a connectionist and localist way by using temporal synchrony. We propose a set of alternatives to temporal synchrony mechanisms that instead use short signatures. This serves two functions: it allows us to explore an additional biologically plausible alternative, and it allows us to extend and improve the capabilities of these models. These extensions model the human ability to both perform unification and handle multiple instantiations of logical terms. To verify our model's feasibility, we simulate it with a computer system modeling simple, neuron-like computations.