We consider decentralized power control in fading multiple-access channels (MAC). When compared to a centralized MAC, solving the optimal power control for a decentralized system is difficult even for moderate number of users. Good thumb-rules for decentralized power control are available in literature, which are also asymptotically tight in the number of users. In this paper, we first derive a structural property that any optimal decentralized power control scheme must follow and use this property to suggest a modified power control scheme. Numerical results suggest that the scheme we propose outperforms the existing ones.