The mobility of water within the microstructure of hardened cement paste has been at the center of a long-lasting debate, motivated by the need to understand the fundamental mechanisms that play a role in drying, shrinkage, creep, and thermal expansion. Our H-1 NMR results show for the first time that externally applied pressure can lead to migration of water within the microstructure (microdiffusion). Upon compression, the gel water signal decreases. For the most part, this is accommodated by a corresponding increase in the signal of water in larger, interhydrate, and capillary spaces. However, there is also an increase in the signal corresponding to the water in most confined spaces. Normally, such tiny spaces are classified as hydrate interlayers. However, we do not conclude that there is a significant increase in interlayer water. Rather, we attribute this part of the increase to a rearrangement of the microstructure upon compression with some water confined in increasingly small gel pore spaces. These findings show that the deformability of the microstructure (C-S-H gel) at the expense of gel porosity may explain part of the macroscopic deformations due to short-term creep.