We show that oxygen vacancies are not necessary for the formation of E' centers in amorphous SiO₂ and that a single O deficiency can lead to two charge traps. Employing molecular dynamics with a reactive potential and density functional theory, we generate an ensemble of stoichiometric and oxygen-deficient amorphous SiO₂ atomic structures and identify low-energy network defects. Three-coordinated Si atoms appear in several low-energy defects both in stoichiometric and O-deficient samples where, in addition to the neutral oxygen vacancy, they appear as isolated defects.