This paper presents a new progressive distributed estimation scheme (DES) along with the power scheduling among sensors under AWGN channels. The progressive DES consists of a transmission bit allocation scheme and a quasi best linear unbiased estimate (BLUE) of the unknown parameter at each sensor. This scheme is shown to outperform the traditional progressive DES. Moreover, the power scheduling among sensors, which minimizes the total transmission power subject to the desired MSE performance tolerance, is formulated as a convex problem and the optimal solution is derived analytically.