A problem of reducing interval uncertainty is considered by an approach of cutting off equal parts from the left and right. The interval contains admissible values of an observed object’s parameter. The object’s parameter cannot be measured directly or deductively computed, so it is estimated by expert judgments. Terms of observations are short, and the object’s statistical data are poor. Thus an algorithm of flexibly reducing interval uncertainty is designed via adjusting the parameter by expert procedures and allowing to control cutting off. While the parameter is adjusted forward, the interval becomes progressively narrowed after every next expert procedure. The narrowing is performed via division-by-q dichotomization cutting off the q–1-th parts from the left and right. If the current parameter’s value falls outside of the interval, forward adjustment is canceled. Then backward adjustment is executed, where one of the endpoints is moved backwards. Adjustment is not executed when the current parameter’s value enclosed within the interval is simultaneously too close to both left and right endpoints. If the value is “trapped” like that for a definite number of times in succession, the early stop fires.