An increasing number of proteins that contain topological knots have been identified over the past two decades; however, their folding mechanisms are still not well understood. UCH-L1 has a 5$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$-knotted topology. Here, we constructed a series of variants that contain a single tryptophan at different locations along the polypeptide chain. A study of the thermodynamic properties of the variants shows that the structure of UCH-L1 is remarkably tolerant to incorporation of bulky tryptophan side chains. Comprehensive kinetic studies of the variants reveal that they fold via parallel pathways on which there are two intermediate states very similar to wild-type UCH-L1. The structures of the intermediate states do not change significantly with mutation and therefore occupy local minima on the energy landscape that have relatively narrow basins. The kinetic studies also establish that there are considerably more tertiary interactions in the intermediate states than results from previous NMR studies suggested. The two intermediates differ from each other in the extent to which tertiary interactions between the highly stable central β-sheet and flanking α-helices and loop regions are formed. There is strong evidence that these states are aggregation prone. The transition states from both I$\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ and I$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ to the native state are plastic and change with mutation and denaturant concentration. Previous studies indicated that the threading event that creates the 5$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ knot occurs during these steps, suggesting that there is a broad energy barrier consistent with the chain undergoing some searching of conformational space as the threading takes place.