The degradation of blood clots is a tightly regulated process. If the mesh of fibrin fibers securing the clot degrades too slowly, thrombi can form, leading to heart attack or stroke. If the fibrin degrades too quickly, excessive bleeding may occur. We study fibrinolysis (the degradation of fibrin by the main fibrinolytic enzyme, plasmin) using a multi-scale mathematical model intended to answer the following question: Why do coarse clots composed of thick fibers lyse more quickly than fine clots composed of thin fibers, despite the fact that individual thin fibers lyse more quickly than individual thick fibers? We use stochastic methods to model lytic processes on scales ranging from individual fiber cross section to whole clot. We find that while fiber number does have an effect on lysis rate, it is not simply "fewer fibers equals faster lysis", as many biologists suggest. In fact, the number of tissuetype plasminogen activator molecules (tPA, an enzyme that converts plasminogen to plasmin) relative to the clot surface area exposed to the tPA strongly influences lysis speeds. We also predict how many plasmin molecules can be produced by a single tPA molecule, how long it takes a given number of plasmin molecules to degrade a single fibrin fiber, and how patterns and speeds of lysis (both on an individual fiber and clot scale) vary under a range of conditions. This last point is of particular interest for development of treatments for occlusive blood clots. Often, a bolus of tPA is injected near the thrombus, in an attempt to initiate therapeutic lysis. Our model predicts other potential targets for future research on effective therapeutic strategies for degrading blood clots.