OBJECTIVES: To test the hypothesis of Burstone and Koenig that a three-bracket geometry can be simplified into two adjacent two-bracket geometries, to evaluate the impact of a third bracket on two-bracket geometries, to identify the force systems of 36 three-bracket geometries using archwires of different materials, and to apply these principles to clinical scenarios. MATERIALS AND METHODS: A custom-designed orthodontic force jig supported three force transducers fitted with passive self-ligating brackets (Brackets A, B, and C). In Experiment 1, the force system of a three-bracket geometry was compared with two adjacent two-bracket geometries. In Experiment 2, 36 three-bracket geometries were tested when straight wires of varying materials were engaged. RESULTS: Experiment 1 results showed that the force system of a three-bracket geometry could be simplified into two adjacent two-bracket geometries. Experiment 2 results showed that the impact of the third bracket (Bracket C) affected the force system of the adjacent bracket only (Bracket B), with Bracket C having no statistically significant effect on the force systems at Bracket A. A distinct pattern of forces and moments was found in each of the 36 three-bracket geometries. CONCLUSIONS: In this study, we experimentally validated the hypothesis of Burstone and Koenig, showing that a three-bracket geometry can be simplified into two adjacent two-bracket geometries. The force system of 36 three-bracket geometries was determined, assisting clinicians with better anticipating previously unpredicted and undesirable movements, thereby improving treatment efficiency.