This paper addresses several innovative steps needed in the chirp scaling and extended chirp scaling (ECS) algorithms in order to process staring Spotlight TerraSAR-X (TSX) images with 21 cm azimuth resolution and 300 MHz range bandwidth. The aspects that need of special consideration are the 2D phase truncation in frequency domain of ECS, the element pattern of the antenna array, the curved orbit, the stop-and-go approximation, and the troposphere. All these aspects are expounded in detail and a solution is given for each of them. The suggested corrections are applied at raw data level, hence easing the integration within the existing TSX processor. Real data acquired by TSX in the experimental staring Spotlight mode are used to validate the proposed methodology.