A compact $X$-band two-stage rf pulse compression system has been successfully designed, fabricated, and tested at Tsinghua $X$-band high-power test stand. The pulse compression system consists of a correction cavity chain, a first-stage, and a second-stage storage cavity. The correction cavity chain adopts a new design whose transmission loss and length are reduced by half compared with the old one. A detuning device is applied to the second-stage storage cavity so that the system can work in one-stage or alternatively two-stage compression mode. In the one-stage compression mode, a 150-ns, 70-MW flattop output, with a standard deviation of 1.5% in amplitude and 1\ifmmode^\circ\else\textdegree\fi{} in phase, was generated with a gain factor of 3. In the two-stage compression mode, a first two-stage pulse compression experiment with correction cavities in the $X$ band was performed. A peak power of 320 MW was achieved with a gain factor of 9.7 and full-width at half-maximum pulse durations of 53 ns.