In this paper, we present a method to align optical fibers within 0.2 μm of the optimal position, using tube laser bending and in situ measuring of the coupling efficiency. For near-UV wavelengths, passive alignment of the fibers with respect to the waveguides on photonic integrated circuit chips does not suffice. In prior research, it was shown that permanent position adjustments to an optical fiber by tube laser bending meets the accuracy requirements for this application. This iterative alignment can be done after any assembly steps. A method was developed previously that selects the optimal laser power and laser spot position on the tube, to minimize the number of iterations required to reach the target position. In this paper, that method is extended to the case where the absolute position of the fiber tip cannot be measured. By exploiting the thermal expansion motion at a relatively low laser power, the fiber tip can be moved without permanent deformation (only elastic strain) of the tube. An algorithm has been developed to search for the optimal fiber position, by actively measuring and maximizing the coupling efficiency. This search is performed before each bending step. Experiments have shown that it is possible to align the fiber with an accuracy of 0.2 μm using this approach.