Recently proposed fast template matching techniques employ rejection schemes derived from lower bounds on the match measure. This paper generalizes that idea and shows that in addition to lower bounds, upper bounds on the match measure can be used to accelerate the search. An algorithm is proposed that utilizes both lower and upper bounds to detect the k best matches in an image. The performance of this dual-bound algorithm is guaranteed; it always detects the k best matches. Theoretical analysis and experimental results show that its runtime compares favorably with previously proposed real-time exact template-matching schemes.