This study presents the RF design of a linear accelerator (linac) operated in single-bunch mode. The accelerator is powered by a compressed RF pulse produced from a SLED-I type RF pulse compressor. The compressed RF pulse has an unflattened shape with a gradient distri-bution which varies over the structure cells. An analytical study to optimize the accelerating structure together with the RF pulse compressor is performed. The optimization aims to maximize the efficiency by minimizing the required RF power from the generator for a given average accelerating gradient. The study shows that, owing to the compressed RF pulse shape, the constant-impedance structure has a similar efficiency to the optimal structure using varying iris apertures. The constant-impedance structure is easily fabricated and is favorable for the design of a linac with a pulse compressor. We utilize these find-ings to optimize the RF design of a X-band linac using the constant-impedance accelerating structure for the Tsinghua Thomson X-ray source facility.