We present an optimized compact finite-difference scheme that has a fourth-order of accuracy but with higher resolving power over a larger range of wavenumbers compared to other traditional finite-difference schemes. In order to realize that, we borrow ideas from Lele’s compact scheme (Lele, 1992) and Tam’s DRP schemes (Tam and Webb, 1993). I.e., we design an optimized finite-difference scheme that uses short stencils but with an optimized coefficient. This way it may help us take advantage of the computer caches without losing higher resolving power. A detailed Fourier analysis on the proposed scheme has been analyzed. A migration impulse response has been tested using our optimized compact finite-difference scheme.