The wavefront of circular dark-hollow-beams with wavelength λ produces a helix of pitch m λ, where m is an integer. But the central phase singularity of such beams can also be generated reducing the pitch by using a modulo operation. When such a beam interferes destructively with an unmodified annular beam of the same order, an incomplete annular beam is produced. The final beam, generated using a standard computer-generated holographic procedure, retains its shape up to 1.5 cm. A potential use of such beams for manipulation of microorganisms has been indicated through a dynamic holographic procedure using a spatial light modulator.