We present the results of a systematic X-ray analysis of a complete and well-defined sample of 23 high-z (z=4-5.5) blazar candidates selected from the CLASS radio survey. In particular, we have complemented the existing archival data (mostly Chandra) with dedicated Swift-XRT observations reaching an almost complete X-ray coverage of the sample. Our aim is to the determination of the nature of all the objects in the sample using X-ray data, since a strong and flat (Gamma