Using high-performance computing techniques and targeted experimental investigation we have developed a predictive crystal-field model of the complex hyperfine structure of ¹⁶⁷Er³+:Y2SiO5 We simultaneously match site-selective spectroscopic data up to 20,000 cm-¹, rotational Zeeman data, and ground- and excited-state hyperfine structure determined from high-resolution Raman-heterodyne spectroscopy on the 1.5 μm telecom transition. We achieve agreement of better than 50 MHz for assigned hyperfine transitions. The successful analysis of the complex hyperfine patterns opens the possibility of systematically searching this whole class of materials for the ZEFOZ transitions that have proved so useful in quantum information applications.