This paper presents a decentralized approach to multi-area power system state estimation using a combination of conventional measurement devices and newer phasor measurement units (PMU). We employ a reduced-order approach to state estimation, wherein the PMU observable and unobservable components of the state vector are estimated separately in each control area. The estimation problem is solved by exchanging information through an improved gossip-based protocol which takes into account the weak measurement coupling between control areas. A detailed analysis of the proposed protocol reveals that the amount of information exchange is always less than the naïve gossip based scheme. We show through simulations on the IEEE 118-bus test system that, in practice, the gossip iterations converge in one iteration regardless of the number of control areas. Our simulations also show that the marginal information exchange is also considerably lower when using the proposed method.