Recent experimental and model work indicates that slowly inactivating potassium currents might play critical roles in generating population rhythms. In particular, slow (<1-4 Hz) rhythms recorded in the hippocampus correlate with oscillatory behaviors in interneurons in this frequency range. Limiting the ion channels to the traditional Hodgkin-Huxley sodium and potassium currents, a persistent sodium current, and a slowly inactivating potassium current, we explore the role of slowly inactivating conductances in a multi-compartmental interneuronal model. We find a rich repertoire of tonic and bursting behaviors depending on the distribution, density and kinetics of this conductance. Specifically, burst frequencies of appropriate frequencies could be obtained for certain distributions and kinetics of this conductance. Robust (with respect to injected currents) regimes of tonic firing and bursting behaviors are uncovered. In addition, we find a bistable tonic firing pattern that depends on the slowly inactivating potassium current. Therefore, this work shows ways in which different channel distributions and heterogeneities could produce variable signal outputs. We suggest that an understanding of the dynamical profiles of inhibitory neurons based on the density and distribution of their currents is helpful in dissecting out the complex roles played by this heterogeneous group of cells.