The present invention provides a data processing system with multiple logical partitions that isolate memory resources for applications contained in the logical partitions. A method is provided for moving a specific memory quantity between two logical partitions by first computing a threshold amount. Then, if the specific memory quantity to be transferred is less than the threshold amount, removing the specific memory quantity from memory assigned in the first partition and adding the specific memory quantity to memory assigned in the second partition. However, if the specific memory quantity is greater than the threshold amount, the method provides for removing an amount equal to the threshold from memory assigned in the first partition and adding that threshold amount to memory assigned in the second partition and repeating the removing and adding steps until the specific memory quantity has been transferred.