The invention relates to iRNA agents, which preferably include a monomer in which the ribose moiety has been replaced by a moiety other than ribose that further includes a tether having one or more linking groups, in which at least one of the linking groups is a cleavable linking group. The tether in turn can be connected to a selected moiety, e.g., a ligand, e.g., a targeting or delivery moiety, or a moiety which alters a physical property. The cleavable linking group is one which is sufficiently stable outside the cell such that it allows targeting of a therapeutically beneficial amount of an iRNA agent (e.g., a single stranded or double stranded iRNA agent), coupled by way of the cleavable linking group to a targeting agent--to targets cells, but which upon entry into a target cell is cleaved to release the iRNA agent from the targeting agent. The inclusion of such a monomer can allow for modulation of a property of the iRNA agent into which it is incorporated, e.g., by using the non-ribose moiety as a point to which a ligand or other entity, e.g., a lipophilic moiety. e.g., cholesterol, is is directly, or indirectly, tethered. The invention also relates to methods of making and using such modified iRNA agents.