A small piston pump is disclosed with a housing having a pair of space and connected pistons therein. The housing has a bore with one of the pistons engaging the bore near one end and has a sleeve mounted therein adjacent the other end. The second piston slides in the bore of the sleeve. One end of the sleeve has an inlet covered by a slit valve and in the end of the sleeve adjacent the slit valve it has a radial outwardly extending opening covered by an elastic band to control the flow of fluid thru the radial outward opening. The other end of the sleeve is carried by the housing bore with a passageway therebetween. A pump output opening is disposed in the housing between the sleeve and the one of the pistons.