Several Crab-type supernova remnants appear to have very bright non-thermal X-ray cores just around the pulsar or expected pulsar. This X-ray brightness is often not matched by a corresponding increase in radio emission. The best example of this phenomenon is in N157B in the LMC. G21.5−0.9 and possibly 3C 58 also show it while the Crab Nebula and 0540−69.3 do not. Some method to enhance the higher energy particles must be present in these objects.