A new sparse array structure based on the recently proposed thinned coprime arrays is proposed to maximize the number of unique lags. The design process involves two stages: the first stage displaces one subarray from its original position for an increase in the number of lags; as the displacement results in the minimum interelement spacing equal to integer multiples of half-wavelength, an additional sensor at a distance of half-wavelength is then added in the displaced subarray to avoid spatial aliasing. The strategic location of the additional sensor results in a significant increase in the overall unique lags which can be utilized for direction-of-arrival estimation (DOA) using compressive sensing based methods. Furthermore, the new structure has excellent performance in the presence of mutual coupling as shown by simulation results.