A nozzle through which air can be pumped into a cushion from a pump includes a housing with a passage extending therein and a space intersecting the passage. A core is put in the space in a sealing and sliding manner for pushing a valve installed in the cushion. The core defines a space. A peripheral hole through which the core communicates the space of the core with the space of the housing. A tubular lip is installed on the housing in a sealing and rotating manner. The tubular lip includes a thread formed on an internal face for engagement with a thread formed on the cushion. A control element includes a cam installed pivotally on the housing for pushing the core and a lever extending from the cam for rotating the cam.