Regulations on radiation limits have been Widely adopted to keep radio transmissions from interfering with each other. Most of them set an upper limit on the total power flux density radiated Within a certain frequency bandwidth,B. But new techniques have given rise to the possibility that some digital transmission systems could cause significant interference to other transmissions without violating the current regulations. This is due to the fact that bursty signals can concentrate most of their energy in a very short pulse with very high power but maintain a low enough average power spectral density, thus meeting the current regulations. New radiation limits are therefore suggested in this paper which set an upper bound on the total energy instead of average power radiated within a certain time period,H, as well as a certain frequency bandwidth,B. It is shown that the current regulations can be easily extended to establish the new limits, and these new limits are essentially identical to the current limits for the traditional continuous-wave signals but can limit the bursty digital signals efficiently as well. Practical consideration for the appropriate length of the time period,H, to be used are discussed, and a few example signals are used to demonstrate the use of the new limits.