In this paper, the data reusing technique which utilizes the LMS algorithm is further investigated. It is shown that a near-optimal performance can be achieved if the number of data reusing runs, M, is made variable. Two modifications are proposed in this paper. The first one is based on updating each individual component of the weight vector with a different step size. This makes the modified algorithm more capable of tracking weight variations than the original algorithm. The second modification makes the algorithm behave initially as the normalized LMS with unity step and at the steady state the algorithm behaves like the LMS with a constant step size. Computer simulations show that the first modification gives the algorithm the capacity to perform better for correlated signals than the original algorithm. Also the second modification is found to give the algorithm the ability to perform very close to optimal for uncorrelated signals.