We use local cosine packets to adaptively segment EEG corresponding to left or right hand index finger movements. The segmentation is constructed by maximizing the Euclidean or Kullback-Leibler distance criterion between the left and right finger movement. The proposed method divides the movement EEG from the C3 and C4 electrodes into nonuniform time segments over a dyadic tree. The most discriminative features are selected from the pruned tree. We observed that the selected segmentation and discriminative components are subject specific. We believe this may eliminate the inter and intrasubject variability when constructing Brain Computer Interfaces. We also found striking asymmetry between feature characteristics and their discrimination power on each hemisphere.