Molecular dynamics simulations combining many microsecond trajectories have recently predicted that a very fast folding protein like lambda repressor fragment lambda(6-85) D14A could have a slow millisecond kinetic phase. We investigated this possibility by detecting temperature-jump relaxation to 5 ms. While lambda(6-85) D14A has no significant slow phase, two even more stable mutants do. A slow phase of lambda(6-85) D14A does appear in mild denaturant. The experimental data and computational modeling together suggest the following hypothesis: lambda(6-85) takes only microseconds to reach its native state from an extensively unfolded state, while the latter takes milliseconds to reach compact beta-rich traps. lambda(6-85) is not only thermodynamically but also kinetically protected from reaching such "intramolecular amyloids" while folding.