In clustered networks of wireless sensors, each sensor collects noisy observations of the environment, quantizes these observations into a local estimate of finite length, and forwards them through one or more noisy wireless channels to the Cluster Head (CH). The measurement noise is assumed to be zero-mean and have finite variance and each wireless hop is modeled as a Binary Symmetric Channel (BSC) with a known crossover probability. A novel scheme is proposed that uses dithered quantization and channel compensation to ensure that each sensor’s local estimate received by the CH is unbiased. The CH fuses these unbiased local estimates into a global one using a Best Linear Unbiased Estimator (BLUE). Analytical and simulation results show that the proposed scheme can achieve much smaller mean square error (MSE) than two other common schemes while using the same amount of energy. The sensitivity of the proposed scheme to errors in estimates of the crossover probability of the BSC channel is studied by both analysis and simulation. We then determine both the minimum energy required for the network to produce an estimate with a prescribed error variance and how this energy must be allocated amongst the sensors in the multihop network.