We observed two compact high-velocity clouds HVC 291+26+195 and HVC 297+09+253 to analyse their structure, dynamics, and physical parameters. In both cases there is evidence for an association with the Leading Arm of the Magellanic Clouds. The goal of our study is to learn more about the origin of the two CHVCs and to use them as probes for the structure and evolution of the Leading Arm. We have used the Parkes 64 m radio telescope and the Australia Telescope Compact Array (ATCA) to study the two CHVCs in the 21 cm line emission of neutral hydrogen. We present a method to estimate the distance of the two CHVCs. The investigation of the line profiles of HVC 297+09+253 reveals the presence of two line components in the spectra which can be identified with a cold and a warm gas phase. In addition, we find a distinct head-tail structure in combination with a radial velocity gradient along the tail, suggesting a ram-pressure interaction of this cloud with an ambient medium. HVC 291+26+195 has only a cold gas phase and no head-tail structure. The ATCA data show several cold, compact clumps in both clouds which, in the case of HVC 297+09+253, are embedded in the warm, diffuse envelope. All these clumps have very narrow HI lines with typical line widths between 2 and 4 km/s FWHM, yielding an upper limit for the kinetic temperature of the gas of T_max = 300 K. We obtain distance estimates for both CHVCs of the order of 10 to 60 kpc, providing additional evidence for an association of the clouds with the Leading Arm.