A self-attaching pump includes a cylinder, a nozzle attached to the cylinder, a piston installed in the cylinder, a rod connected to the piston, a handle with a first end and an opposite second end, a fastener for pivotally connecting the second end of the handle to the rod and a stressing device arranged on the cylinder for stressing the self-attaching pump. There are defined a first value for the distance between the fastener and the first end of the handle, a second value for the length of the elastic element when the stressing does not stress the self-attaching pump and a third value for the distance between the piston and the nozzle when the first end of the handle reaches the stressing device while the stressing device does not stress the self-attaching pump. The first value is larger than the second value that is larger than the third value.