This paper describes a rapid acquisition technique which can be used in direct sequence spread-spectrum systems. It is sequential in nature and is based on a double threshold which defines when a decision can be made. The values of the thresholds change at every examination instant. The procedure makes use of a bound to the partial crosscorrelation function of PN sequences which ensures that only the sequence length needs to be given as far as the PN sequence particulars are concerned. A decision is made only if the probability of error associated with a decision at that point is equal to or better than a prespecified value. Finally, it is shown that most of the computational difficulties associated with the bound as given by a recursive algorithm can be eliminated when using a low-order polynomial approximation to the bound. However, either by using the bound or its polynomial approximation, a significant improvement in the acquisition time is obtained.