Many possible causes of the slow-down have been suggested, and these may be coarsely divided into two groups: 1. Restrictions that build up with the degree of conversion and 2. Inherent restrictions governed by enzyme-substrate interactions. Typical examples of factors from group 1 include product inhibition and depletion of reactive subsets of the insoluble substrate. Here, we focus on group 2 and show how the analysis of the initial (transient) kinetics of cellobiohydrolase 1 (CBH1) provides insight into the rates of different steps in the cellulolytic process. Specifically, we have used real-time measurements of cellulase activity on different insoluble substrates and explicit modeling to show that the early slowdown of CBH1 reflects a balance between rapid adsorption, chain acquisition and processive movement on one hand and a slow off-rate on the other.