Magnetoresistance measurements of Bi wires performed in the magnetic field oriented along the bisector axis revealed unexpected anomalous peaks in a high magnetic field far above the quantum limit of the electrons. By combining a magnetic field and an uniaxial strain, we obtained a modification of the electronic structure; as a result, the quantum limit for light and heavy electrons is changed in a different way. For the case where heavy electrons are in the quantum limit, a correlation between the exit of the lowest Landau level of light electrons and the Lifshitz transition was found.