An improved cleat assembly is disclosed, the assembly containing one or more spring clips configured for releasably securing the assembly to a bicycle pedal or the like. Specifically, the cleat assembly is configured such that an improper over-tightening of the cleat onto the sole of a user's shoe has substantially no effect on the free flexing of the spring clip while it is engaging or disengaging to/from the pedal. In addition, the cleat assembly incorporates one or more soft elastomeric caps that frictionally engage the ground when the user walks about, to provide improved traction and to eliminate undesired wear of critical assembly components. Further, for embodiments of cleat assemblies of the kind incorporating one or more adjustable set screws for adjusting the assemblies' float angles, threaded apertures for the set screws are formed by the confronting surfaces of a plastic upper plate and a metallic bottom plate, wherein the threads are formed only in the plastic upper plate. This allows the upper plate to be conveniently formed of an injection-molded plastic material and the bottom plate to be conveniently stamped from a piece of sheet metal.