Four versions of a β-sheet protein (CD2.d1) have been made, each with a single artificial disulfide bond inserted into hairpin structures. Folding kinetics of reduced and oxidized forms shows bridge position strongly influences its effect on the folding reaction. Bridging residues 58 and 62 does not affect the rapidly formed intermediate (I) or rate-limiting transition (t) state, whereas bridging 33 and 38, or 31 and 41, lowers the t-state energy, with the latter having the stronger influence. Bridging residues 79 and 90 stabilizes both I- and t-states. To assess additivity in the energetic effects of these bridges, four double-bridge variants have also been made. All show precise additivity of overall stability, with two showing additivity when ground states and the rate-limiting t-state are assessed, i.e. no measurable change in the folding mechanism occurs. However, combining 31-41 and 79-90 bridges produces a molecule that folds through a different pathway, with a much more stable intermediate than expected and a much higher t-state barrier. This is explained by the artificial introduction of stabilizing, non-native contacts in the I-state. More surprisingly, for another double-bridge version (58-62 and 79-90) both I- and t-states are less stable than expected, showing that conformational constraints introduced by the two bridges prevent formation of non-native contacts that would otherwise stabilize the I- and t-states, thereby lowering the energy of the folding landscape in the wild-type (unbridged) molecule. We conclude that the lowest energy path for folding has I- and t-state structures that are stabilized by non-native interactions.