Several existing algorithms for squinted sliding spotlight synthetic aperture radar (SAR) suffer from low efficiency, despite their good focusing abilities. Their low speeds are primarily due to the use of wave-number domain (Omega-K) processing after spectrum unfolding in the azimuth frequency domain. Omega-K processing is chosen in these algorithms due to its focusing ability at large squint angles. However, in most scenarios, spaceborne SARs operate with small squint angles that are generally not greater than 5 deg. In these scenarios, Omega-K processing is not necessary and is not preferred due to its computational burden. Thus, in this study, we extend a classic, two-step algorithm based on the chirp -transformation for the efficient processing of SAR data acquired in spaceborne sliding spotlight mode at a small squint angle. The modified azimuth-filtering and focusing processing is used to compensate for the additional Doppler bandwidth caused by the antenna squinting and is described in detail. The simulation results show the good focusing ability of the proposed algorithm and validate the improvement in computational efficiency.