This paper revisits an optimal rate and power allocation problem to maximize throughput in uplink CDMA singlecell packet data communications. First, we show that the widelyaccepted belief that an optimally selected rate always keeps a constant value of the resulting bit energy to the interference plus noise power spectral density ratio is not true in most practical CDMA packet transmission environments, where the packet size varies in proportion to the rate. Then, we derive the rate-dependent optimal bit energy-to-interference- noise power spectral density ratio, based on which we convert the original joint optimization problem of rate and power to an equivalent but simple power allocation problem. Finally, we derive an optimal power allocation strategy by applying the convex optimization theory. Through two instructive examples, we show that the optimality of the well-known bang bang power control, that is, each user (except at most one user) should either transmit his data at the maximum allowed power level or at the minimum required power level meeting the SINR requirement in order to maximize the system throughput, may or may not be true depending on the incorporated channel coding scheme.