Adaptive Random Testing (ART) methods are Software Testing methods which are based on Random Testing, but which use additional mechanisms to ensure more even and widespread distributions of test cases over an input domain. Restricted Random Testing (RRT) is a version of ART which uses exclusion regions and restriction of test case generation to outside these regions. RRT has been found to perform very well, but incurs some additional computational cost in its restriction of the input domain. This paper presents a method of reducing overheads called Forgetting, where the number of test cases used in the restriction algorithm can be limited, and thus the computational overheads reduced. The motivation for Forgetting comes from its importance as a human strategy for learning. Several implementations are presented and examined using simulations. The results are very encouraging.