Poly(3-hydroxybutyrate) (P3HB) is a thermoplastic polyester produced by bacteria. Developing an upscalable melt-spinning process, we found that a controlled crystallization process is crucial for producing P3HB fibers: Primary crystallization has to be completed during the drawing step, while secondary crystallization has to be hindered to prevent brittleness and poor tensile properties. By modifying melt-spinning and drawing, we achieved fibers dominated by longitudinally oriented lamellae rather than spherulitic structures. To better understand the development of macromolecular orientation during fiber forming and annealing, we performed tensile stage and hot stage experiments in combination with wide-angle X-ray diffraction (WAXD). P3HB fibers were subjected to various tensions and temperatures in-situ. In the equatorial 2Theta scan of the WAXD patterns of these fibers, we observed a series of local maxima. In previous literature, the diffraction signals in this region are commonly described as one reflection, assigned to the so-called "beta-form" of P3HB. In contrast we postulate a highly oriented non-crystalline phase P(nc), which is kinetically trapped between the aligned lamellae of the crystalline alpha-phase. In our model, the oriented crystalline phase partially morphs into an oriented P(nc) under stress only. Cyclic change of tension reveals a high degree of reversibility for this transformation. Under heat only, the entrapped, oriented P(nc) gains mobility and thus irreversibly turns into an oriented crystalline phase. When combining stress and heat, the applied tension prevents such a transformation of the oriented P(nc), but it promotes an increase in orientation of the crystalline phase. On the fiber level, annealing under tension results in a higher modulus, while annealing without tension increases plasticity. This is in correspondence with the proposed structural model.