Fully sequential selection procedures have been developed in the field of stochastic simulation to find the simulated system with the best expected performance when the number of alternatives is finite. Kim and Nelson proposed the KN procedure to allow for unknown and unequal variances and the use of common random numbers. KN approximates the raw sum of differences between observations from two systems as a Brownian motion process with drift and uses a triangular continuation region to decide the stopping time of the selection process. In this paper new fully sequential selection procedures are derived that employ a more effective sum of differences, which is called a controlled sum. Two provably valid procedures and an approximate procedure are described. Empirical results and a realistic illustration are provided to compare the efficiency of these procedures with other procedures that solve the same problem.