The acquisition of CDMA signals in adverse mobile communication channels has been studied for more than five decades. However, the introduction of new standard proposals for the future European satellite system (i.e., Galileo) and for the modernized GPS has triggered new interest in fast and reliable acquisition strategies for CDMA systems with very high spreading factors (e.g., length of 10230 chips or higher). Typically, the double-dwell serial search strategies have been preferred for CDMA signal acquisition. Few papers have addressed also the problem of hybrid and parallel search strategies, but typically, the choice of the best number of dwells has not been discussed. The goal of this paper is to introduce a generic method for the computation of the mean acquisition time (MAT) for multiple-dwell hybrid-search acquisition blocks and to compare the performance of several multiple-dwell structures for CDMA systems with high spreading factors. It will be shown here that increasing the number of dwells does not always increase the performance from the point of view of the MAT. We also discuss the influence of various parameters on the selection of the multiple-dwell strategy and we present simulation results for a realistic Galileo signal.