1 Energy efficiency of fixed-rate transmissions is studied in the presence of queueing constraints and channel uncertainty. It is assumed that neither the transmitter nor the receiver has channel side information prior to transmission. The channel coefficients are estimated at the receiver via minimum mean-square-error (MMSE) estimation with the aid of training symbols. It is further assumed that the system operates under statistical queueing constraints in the form of limitations on buffer violation probabilities. The optimal fraction of power allocated to training is identified. Spectral efficiency-bit energy tradeoff is analyzed in the low-power and wideband regimes by employing the effective capacity formulation. In particular, it is shown that the bit energy increases without bound in the lowpower regime as the average power vanishes. On the other hand, it is proven that if sparse multipath fading with bounded number of independent resolvable paths is experienced, the bit energy diminishes to its minimum value in the wideband regime as the available bandwidth increases. For this case, expressions for the minimum bit energy and wideband slope are derived. Overall, energy costs of channel uncertainty and queueing constraints are identified.