Transport properties of particles in confining geometries show very specific characteristics as lateral drift, oscillatory movement between lateral walls or the deformation of flexible fibers. These dynamics result from viscous friction with transversal and lateral channel walls inducing strong flow perturbations around the particles that act like moving obstacles. In this paper, we modify the fiber shape by adding an additional, small fiber arm, which leads to T- and L-shaped fibers with only one or, respectively, zero symmetry axes and investigate the transport properties. For this purpose, we combine precise microfluidic experiments and numerical simulations based on modified Brinkman equations. Even for small shape perturbations, the transport dynamics change fundamentally and formerly stable configurations become unstable, leading to non-monotonous fiber rotation and lateral drift. Our results show that the fundamental transport dynamics change with respect to the level of fiber symmetry, which thus enables a precise control of particle trajectories and which can further be used for targeted delivery, particle sorting or capture inside microchannels. Copyright (C) EPLA, 2019