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In the well-known distributed target-SIR tracking power control algorithm, when the target-SIR requirements are not reachable for all users, all non-supported users (those who do not reach their target SIRs) transmit at their maximum power. Such users inefficiently consume their energies, and introduce unnecessary interference to others, which in turn unnecessarily increases the number of non-supported users. To deal with this, the smallest number of users should be removed due to infeasibility of the system (gradual removal problem). We present a new distributed constrained power control (DCPC) algorithm to address the gradual removal problem. The basic idea is that any transmitting user whose required transmit power for reaching its target-SIR exceeds its maximum power is temporarily removed. Each temporarily removed user resumes its transmission if its required transmit power for reaching its target-SIR goes below a given threshold (lower than its maximum power). This threshold is determined by each removed user in a distributed manner using only local information. We will show that our proposed algorithm has at least one-fixed point (i.e., its convergence can be guaranteed), and at the equilibrium where the algorithm converges, all transmitting users (the users whose transmit powers are greater than zero) reach their target SIRs consuming the minimum aggregate transmit power. Furthermore, in contrast to the existing DCPC algorithms, no user is unnecessarily removed in our proposed scheme, i.e., it is efficient. Our simulation results confirm our analytic developments and show that our scheme outperforms the existing DCPCs in addressing the gradual removal problem, in terms of convergence, outage probability and power consumption.