The Adaptive Laplace and Analytic Radioactivity Analysis [ALARA] code has been developed as the next link in the chainb of DKR1-3 radioactivity codes. Its methods address the criticisms of DKR while retaining its best features. While DKR ignored loops in the transmutation/decay scheme to preserve the exactness of the mathematical solution, ALARA incorporates new computational approaches without jeopardizing the most important features of DKR's physical modelling and mathematical methods.4 The physical model uses “straightened-loop, linear chains” to achieve the same accuracy in the loop solutions as is demanded in the rest of the scheme.5 In cases where a chain has no loops, the exact DKR solution is used. Otherwise, ALARA adaptively choses between a direct Laplace inversion technique and a Laplace expansion inversion technique to optimize the accuracy and speed of the solution. All of these methods result in matrix solutions which allow the fastest and most accurate solution of exact pulsing histories. Since the entire history is solved for each chain as it is created, ALARA achieves the optimum combination of high accuracy, high speed and low memory usage.