<p>Aspiration catheters generally comprise a tube or shaft with an aspiration opening at or near its distal end and a suction device that is at or near the proximal end of the catheter. An aspiration lumen extends from the suction device to the aspiration opening. The aspiration catheter can be associated with an extendable device such that their functions can be combined advantageously. The extendable device can function as a treatment structure and/or as a flow modifier. A treatment structure can be used to expand a constriction in a vessel or to deliver a treatment element into the vessel. A flow modifier generally controls the flow to decrease flow in the vicinity of the aspiration opening to improve the efficiency of the aspiration. Various relationships between the extendable structure and the aspiration catheter are described. Balloons can be used effectively as treatment structures or flow modifiers, although self-extending stents can be used as treatment structures and flaps or the like can be used as flow modifiers.</p>