An improved method of acquisition of pseudonoise signals (RARASE) is described and analyzed. This method is an outgrowth of the RASE method, rapid acquisition by sequential estimation. In the new method, the known recursion relation of the PN signal is used to determine if a short estimate of the state of the received PN signal is probably correct and if, consequently, an attempt should be made to track with that estimate. A high proportion of the incorrect initial state estimates can be discarded with relatively simple logic. Analyses are provided for a range of implementations from the simplest, a single 3-input modulo-2 gate, to multiple logic gates and for both a simple in-lock detector and a sequential detector. Significant improvement in acquisition time is shown for long PN signals and for the signal-to-noise range of -13 dB to +3 dB. Acquisition time reduction by a factor of 7.5 is calculated for a PN signal of length2^{15}-1bits compared to the sequential estimation (RASE) method using a simple in-lock detector. Reduction by factors of 1.5 to 3.5 is calculated using the sequential detector.