Emerging multimedia services in cellular radio systems introduce a variable transmission rate, which raises the problem of controlling transmission rates in a spectrally efficient way. In this paper, we formulate the problem into a combined power and rate control, for which we suggest two different algorithms. In the first one, we derive an algorithm applying the Lagrangian relaxation technique. In the other method, called selective power control, we extend a fixed rate power control algorithm to solve the problem. Computational experiments carried out on a CDMA system indicate that the proposed algorithms give satisfying performance in terms of system throughput, outage probability and transmission power consumption.