Abstract: It has been suggested that Planck-scale "spacetime foam" could have significant macroscopic consequences, perhaps even offering a way to address the cosmological constant problem. Â I will describe progress in constructing a locally spherically symmetric minisuperspace model with a positive cosmological constant that may shed light on these questions. Classically, the model includes "foamy" spacetimes that contain both expanding and contracting regions. Quantum mechanically, the Wheeler-DeWitt equation is relatively tractable, and has stationary solutions in which the amplitudes for such "foamy" regions are large and the probability currents are very small. While the results so far are incomplete, the approach seems promising.