This paper investigates intra-adaptive wavelets for video coding with frame-adaptive motion-compensated lifted wavelet transforms. With motion-compensated lifted wavelets, the temporal wavelet decomposition operates along motion trajectories. However, valid trajectories for efficient multi-scale filtering have a finite duration in time. This is due to well known effects like occlusions or inaccurate motion estimation. These discontinuities may generate many non-zero wavelet coefficients when a transform with a fixed dyadic structure is used. To investigate the advantage of an adaptive transform, we introduce intra macroblocks in the frame-adaptive lifting steps. Depending on the rate-distortion costs at a given macroblock location, we choose the number of wavelet decomposition levels locally. We discuss motion-compensated lifted wavelets that are frame- and intra-adaptive. We evaluate the efficiency of intra-adaptive wavelets when frame-adaptive motion-compensated wavelets are used. We observe that intra-adaptivity is rate-distortion efficient for discontinuities that cannot be handled by frame-adaptivity.