As low power, low cost, and longevity of transceivers are major requirements in wireless sensornetworks, optimizing their design under energy constraints is of paramount importance. To this end,we develop quantizers under strict energy constraints to effect optimal reconstruction at the fusioncenter. Propagation, modulation, as well as transmitter and receiver structures are jointly accounted forusing a binary symmetric channel model. We first optimize quantization for reconstructing a singlesensor's measurement, and deriving the optimal number of quantization levels as well as the optimalenergy allocation across bits. The constraints take into account not only the transmission energy butalso the energy consumed by the transceiver's circuitry. Furthermore, we consider multiple sensorscollaborating to estimate a deterministic parameter in noise. Similarly, optimum energy allocation andoptimum number of quantization bits are derived and tested with simulated examples. Finally, we studythe effect of channel coding on the reconstruction performance under strict energy constraints and jointlyoptimize the number of quantization levels as well as the number of channel uses.