A method of and system for searching for position determination signals using a plurality of progressively more sensitive search modes comprising a first level mode, a second mode, and at least one higher level mode. If any of the search window parameters exceed prescribed limits, a first level search is performed, and the search window parameters are refined responsive to the ensuing search results so they are within the prescribed limits. Then, the second level search is performed, and measurements derived from the ensuing search results. If the measurements satisfy selected measurement sufficiency criteria, additional searching within the position fix attempt is avoided. If the measurements do not satisfy the selected measurement sufficiency criteria, a higher level, more sensitive search is performed.