The use of acoustic resonators is an effective way to control cavity resonances in small enclosures. One popular device is the long, T-shaped acoustic resonator which consists of three branches. Two branches (referred to as ‘‘Branch-1’’ and ‘‘Branch-2’’) are co-axial and both have one open end and one closed end, and the third branch (referred to as ‘‘Branch-3’’) is perpendicular to the co-axis and has two open ends. In practical cavity noise control, the optimal position of Branch-3, i.e., the length of Branch-1 or Branch-2 is determined by the mode shape of the controlled cavity mode, and the length of Branch-3 is typically chosen to be as short as possible to minimize the occupied space of the resonator. If the cross-sectional areas are given, the only design parameter is the length of Branch-1 or Branch-2. In this study, three new models are developed to calculate the end corrections for the three branches. The novel theory is also used to design long T-shaped acoustic resonators for control. In addition to the fundamental acoustic resonator mode, higher frequency resonances of the resonator can be used to target a specific cavity mode for control. Several tests are conducted to experimentally evaluate and validate these new models.