Using the potential of two unprecedented missions, Solar Terrestrial Relations Observatory (STEREO) and Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI), we study three well-observed fast coronal mass ejections (CMEs) that occurred close to the limb together with their associated high-energy flare emissions in terms of RHESSI hard X-ray (HXR) spectra and flux evolution. From STEREO/EUVI and STEREO/COR1 data, the full CME kinematics of the impulsive acceleration phase up to ~4 R _sun is measured with a high time cadence of <=2.5 minutes. For deriving CME velocity and acceleration, we apply and test a new algorithm based on regularization methods. The CME maximum acceleration is achieved at heights h <= 0.4 R _sun, and the peak velocity at h <= 2.1 R _sun (in one case, as small as 0.5 R _sun). We find that the CME acceleration profile and the flare energy release as evidenced in the RHESSI HXR flux evolve in a synchronized manner. These results support the "standard" flare/CME model which is characterized by a feedback relationship between the large-scale CME acceleration process and the energy release in the associated flare.