The unfolded state of globular proteins is not well described by a simple statistical coil due to residual structural features, such as secondary structure or transiently formed long-range contacts. The principle of minimal frustration predicts that the unfolded ensemble is biased toward productive regions in the conformational space determined by the native structure. Transient long-range contacts, both native-like and non-native-like, have previously been shown to be present in the unfolded state of the four-helix-bundle protein acyl co-enzyme binding protein (ACBP) as seen from both perturbations in nuclear magnetic resonance (NMR) chemical shifts and structural ensembles generated from NMR paramagnetic relaxation data. To study the nature of the contacts in detail, we used paramagnetic NMR relaxation enhancements, in combination with single-point mutations, to obtain distance constraints for the acid-unfolded ensemble of ACBP. We show that, even in the acid-unfolded state, long-range contacts are specific in nature and single-point mutations affect the free-energy landscape of the unfolded protein. Using this approach, we were able to map out concerted, interconnected, and productive long-range contacts. The correlation between the native-state stability and compactness of the denatured state provides further evidence for native-like contact formation in the denatured state. Overall, these results imply that, even in the earliest stages of folding, ACBP dynamics are governed by native-like contacts on a minimally frustrated energy landscape.