Transition state structures in two-state folding are not experimentally accessible (by definition they are the least populated along the reaction coordinate), but the folding sub-ensembles in downhill folding processes are theoretically distinguishable by spectroscopy. The 40-residue protein BBL, which is an independently folding domain from the E2 subunit of the 2-oxoglutarate dehydrogenase multi-enzyme complex of E. coli, has been experimentally shown to fold globally downhill. Also, a mutant of lambda repressor protein has been shown to shift from downhill to two-state upon changing the temperature/solvent conditions. However, the status of BBL as a downhill-folding protein, and by extension the existence of naturally occurring downhill folders, has been controversial. The current controversy arises from the fact that the only way a protein can be labeled as two-state or downhill is by analyzing the experimental data with models that explicitly deal with these two situations, i.e. by allowing the barrier heights to vary. Unfortunately, most of the experimental data so far have been analyzed with a simple chemical two-state model. In other words, the presence of a rather large free energy barrier has been pre-assumed, ruling out the possibility of identifying downhill or globally downhill protein folding. This is critical because any sigmoidal unfolding curve, irrespective of the degree of cooperativity, can be fit to a two-state model. Kinetically, the presence of a barrier guarantees a single-exponential, but not vice versa. Nevertheless, in some proteins such as the yeast phosphoglycerate kinase and a mutant human ubiquitin, non-exponential kinetics suggesting downhill folding have been observed.