The present invention relates to a technique for accessing memory units in a data processing apparatus. The data processing apparatus comprises of plurality of memory units for storing data values, a processor core for issuing an access request specifying an access to be made to the memory units in relation to a data value, and a memory controller for performing the access specified by the access request. Attribute generation logic is provided for determining from the access request one or more predetermined attributes verifying which of the memory units should be used when performing the access. However, the memory controller does not wait until such determination has been performed by the attribute generation logic before beginning the access. Instead, prediction logic is arranged to predict the one or more predetermined attributes, and clock generation logic is responsive to the predictive predetermined attributes from the prediction logic to select which one of the memory units is to be clocked during performance of the access, and to issue a clock signal to that memory unit. Checking logic is then provided to determine whether the predetermined attributes generated by the attribute generation logic agree with the predicted predetermined attributes, and if not, to reinitiate the access, in which event the clock generation logic is arranged to reselect one of the memory units using the predetermined attributes as determined by the attribute generation logic. This approach enables high speed processing of access requests, whilst achieving significant power savings over prior art systems where multiple memory units are clocked speculatively in parallel.