An optimum power and rate allocation rule for cellular code division multiple access (CDMA) downlink networks is derived; it minimises mean transmission delay of the active users with different channel qualities under the constraints of total transmission power and the required signal-to-interference ratio. The proposed rule states that the power assigned to a user is inversely proportional to the square root of the user's channel quality factor, whereas the rate assigned to a user is proportional to the square root of the user's channel quality factor. The amount of reduction in average mean transmission delay by the proposed optimum allocation rule against the equal rate allocation with power control and the equal power allocation with rate control is also derived for the case when each user undergoes shadowing, path loss and inter-cell interference. It is shown that the proposed allocation rule not only achieves the minimum mean transmission delay, but also minimises the probability of the data rate being less than a tolerable threshold, against the equal rate or equal power allocation schemes.