A folded camera that includes two light folding elements such as prisms and an independent lens system, located between the two prisms, which includes an aperture stop and a lens stack. The lens system may be moved on one or more axes independently of the prisms to provide autofocus and/or optical image stabilization for the camera. The shapes, materials, and arrangements of the refractive lens elements in the lens stack may be selected to capture high resolution, high quality images while providing a sufficiently long back focal length to accommodate the second prism.