The development of magnetically-powered microswimmers that mimic the swimming mechanisms of microorganisms are important for lab-on-a-chip devices, robotics, and next-generation minimally-invasive surgical interventions. Governed by their design, most previously described untethered swimmers can be maneuvered only by varying the direction of applied rotational magnetic fields. This constraint makes even state-of-the-art swimmers incapable of reversing their direction of motion without a prior change in the direction of field rotation, which limits their autonomy and ability to adapt to their environments. Also, owing to constant magnetization profiles, swarms of magnetic swimmers respond in the same manner, which limits multi-agent control only to parallel formations. Herein, we present a new class of microswimmers which are capable of reversing their direction of swimming without requiring a reversal in direction of field rotation. These swimmers exploit heterogeneity in their design and composition to exhibit reversible bidirectional motion determined by the field precession angle. Thus, the precession angle can be used as an independent control input for bi-directional swimming. Design variability is explored in the systematic study of two swimmer designs with different construction. Two different precession angles are observed for motion reversal, which is exploited to demonstrate independent control of the two swimmer designs.