Optical gradient forces generated by fast steerable optical tweezers are highly effective for sorting small populations of cells in a lab-on-a-chip environment. The presented system can sort a broad range of different biological specimens by an automated optimisation of the tweezer path and velocity profile. The optimal grab positions for subsequent trap and cell displacements are estimated from the intensity of the bright field image, which is derived theoretically and proven experimentally. We exhibit rapid displacements of 2 μm small mitochondria, yeast cells, rod-shaped bacteria and 30 μm large protoplasts. Reliable sorting of yeast cells in a microfluidic chamber by both morphological criteria and by fluorescence emission is demonstrated.