A method and system for canceling extraneous signals in a nuclear quadrupole resonance (NQR) system used for the detection of explosives and drugs. A specimen is irradiated with a specific sequence of electromagnetic pulses, referred to as a spin-locked inversion mid-echo (SLIME) pulse sequence with each pulse having a specified phase and duration. The pulses are separated by specified time intervals. The SLIME pulse sequence has a single excitation pulse. As a result of the characteristics of the SLIME pulse sequence, if the target substance to be detected is present in the specimen, sets of oppositely-phased NQR echo signals are generated from the target substance. NQR echo signals of one phase are subtracted from NQR echo signals having the opposite phase, rendering a cumulative echo signal, and simultaneously subtracting out the same-phase extraneous signal.