In this work, we study the effect of inserting spatially local temporal adaptivity to motion compensated frame adaptive transforms for video coding. Motion compensation aligns the temporal wavelet decomposition along motion trajectories. However, valid trajectories for an efficient multi-scale filtering have a finite duration in time. This is due to well known effects like occlusions or inaccurate motion estimation. Hence, the signal encountered by the temporal wavelet transform can be seen as a piecewise-smooth signal. The breakpoints of this signal, may generate many wavelet coefficients when transforms with a fixed number of subbands are used. Theoretical results indicate that adaptive transformations can do better with this kinds of signals than simple wavelet transforms. In this paper we discuss the usage of a motion compensated lifting scheme that adapts the number of decomposition levels depending on the spatial location by means of a R-D criteria. This adaptation is done by introducing the use of Intra Macroblocks in the lifting steps. This allows to virtually adapt the GOP length used for the wavelet decomposition in a local fashion. A detailed analysis of the benefits in terms of R-D and visual quality corroborates the expected improvement suggested by theory on the compression of piecewise smooth signals.