Acquisition of an incoming long pseudo-noise (PN) code signal requires a fast hypothesis testing function for a large number of code phase hypotheses. Since a receiver has limited hardware resources (in terms of number of correlators and computational capacity) in practice, fast PN code acquisition is not an easy goal to achieve. In this paper, we propose a double dwell search scheme, where a 2D compressed correlator (TDCC) tests a number of coherently combined neighboring code phase hypotheses and Doppler frequency hypotheses at a time in the 1st dwell search, and all individual hypotheses found in the 1st dwell search are tested in the 2nd dwell search using a conventional correlator. We present theoretical performance analysis of the proposed technique and Monte Carlo simulation results to demonstrate the performance of the proposed technique with respect to detection threshold and non-coherent accumulation number and to compare it to the conventional double dwell search technique.