The folding mechanism of a protein is determined by its primary sequence. Yet, how the mechanism is changed by a mutation is still poorly understood, even for basic secondary structures Such as beta-hairpins. We perform an extensive simulation study of the effects of mutating the GB1 beta-hairpin into Trpzip4 (Y5W, F12W, V14W) on the folding mechanism. While Trpzip4 has a much more stable native state due to very strong hydrophobic interactions of the side chains, its folding rate does not differ significantly from the wild type beta-hairpin. We sample the free-energy landscapes of both hairpins with Replica Exchange Molecular Dynamics (REMD) and identify the four (meta)stable states (U, H, F, and N). Using Transition Path Sampling (TPS), we then harvest ensembles of unbiased pathways between the H and F states and between the F and IN states to investigate the unbiased folding mechanisms. In both hairpins, the hydrophobic collapse (U-H) is followed by the middle hydrogen bond formation (H-F), and finally a closing of the strands in a zipperlike fashion (F-N). For the Trpzip4, the path ensembles indicate that the final F-N step is much more difficult than for GB1 and involves partial unfolding, rezipping of hydrogen bonds, and rearrangement of the Trp-14 side chain. For the rate-limiting (H-F) step, the path ensembles show that in GB1 desolvation and strand Closure go hand in hand, while in Trpzip4 desolvation is decoupled from strand closure. Nevertheless, likelihood maximization shows that the reaction coordinate for both hairpins remains the interstrand distance. We conclude that the folding mechanism of both hairpins is a combination of hydrophobic collapse and zipping of hydrogen bonds but that the zipper mechanism is more visible in Trpzip4. A major difference between the two hairpins is that in the transition state of the rate-limiting step for Trpzip4 one tryptophan is exposed to the solvent due to steric hindrance, making the folding mechanism more complex and leading to an increased F-N barrier. Thus, our results show in atomistic detail how a mutation leads to a different folding mechanism and results in a more frustrated folding free-energy landscape.