The response of a reactor to step changes in δk is reviewed for two cases; small positive cangesh in δk, and changes in 8k greater than β. Analytical expressions are derived which give the negative change in δk required to terminate each type of excursion. Expressions for obtaining power overshoot are also obtained for each case for various types of δk removal. The analytical results are confirmed by more exact calculations with an analog and a digital computer. It is shown that to terminate an excursion produced by a change in δk <β, it is only necessary to reduce δk at a rate such that zero δk is reached in about 21/2 sec. The fact that, to terminate a super-prompt-critical excursion, it is only necessary to reduce δk to a value equal to approximately β, is demonstrated analytically.