Ultra-high-resolution wall-sized displays (" ultra-walls ") are effective for presenting large datasets, but their size and resolution make traditional pointing techniques inadequate for precision pointing. We study mid-air pointing techniques that can be combined with other, domain-specific interactions. We first explore the limits of existing single-mode remote pointing techniques and demonstrate theoretically that they do not support high-precision pointing on ultra-walls. We then explore solutions to improve mid-air pointing efficiency: a tunable acceleration function and a framework for dual-precision techniques, both with precise tuning guidelines. We designed novel pointing techniques following these guidelines, several of which outperform existing techniques in controlled experiments that involve pointing difficulties never tested prior to this work. We discuss the strengths and weaknesses of our techniques to help interaction designers choose the best technique according to the task and equipment at hand. Finally, we discuss the cognitive mechanisms that affect pointing performance with these techniques.