Refinement of databases of connected stationary points to describe global kinetics is discussed for the GB1 hairpin peptide modelled by an empirical potential and an implicit solvent model. Two approaches to the removal of artificial kinetic frustration caused by undersampling are separately applied to an initial database of stationary points. We consider both additional sampling between minima close in energy but separated by high barriers, and the removal of stationary points that do not contribute significantly to the calculated rate constants for the initial database. Results from these two approaches are found to be consistent: the transition networks produced in both cases exhibit structure-seeking properties because most of the initial frustration is removed. Excluding stationary points from the initial database that do not appear on kinetically relevant paths proves to be much less computationally expensive than subsequently finding better connections for them. After application of a coarse-graining scheme that groups together sets of minima separated by low barriers, the calculated folding time is consistent with expectations for β-hairpins modelled using implicit solvent. The folding mechanism corresponding to the most significant kinetic paths involves early compaction, followed by formation of the turn and then completion of the hydrophobic core.