Cost-effective health care depends on high-quality triage. The most challenging aspect of triage, which GPs confront on a regular basis, is diagnosing rare but serious disease. Failure to shoulder any risk in this situation overloads the health system and subjects patients to unnecessary investigation. Adopting too high a risk threshold leads to missed cases, late diagnosis, and sometimes avoidable death. It also undermines the credibility of primary care practitioners. Quantification of diagnostic risk suggests there is a potential risk gap between the maximum certainty with which GPs can assess the risk of serious disease at presentation and the minimum certainty required by many health systems for further investigation or hospital referral. Physician gut-feeling and diagnostic safety netting are often employed to fill the gap. Neither strategy is well defined or well supported by evidence. It should be possible to reduce the diagnostic risk gap cost-effectively by adopting more explicit diagnostic algorithms and providing better GP access to new diagnostic technologies. It is also essential, given the decreasing experience of triage clinicians employed in a number of countries, that a teachable evidence base is constructed for gut feeling and diagnostic safety netting. However, this construction of an evidence base requires very large-scale studies, and the global primary care research community remains small. The challenge therefore needs to be met by urgent and effective international collaboration.