The development of resistant strains of HIV is the most significant barrier to effective long-term treatment of HIV infection. The most common causes of resistance development are patient noncompliance and pre-existence of resistant strains. In this paper, methods of antiviral regimen switching are developed that minimize the risk of pre-existing resistant virus emerging during therapy switches necessitated by virological failure. Two distinct cases are considered; a single previous virological failure and multiple virological failures. These methods use optimal control approaches on experimentally verified mathematical models of HIV strain competition and statistical models of resistance risk. It is shown that, theoretically, order-of-magnitude reduction in risk can be achieved, and multiple previous virological failures enable greater success of these methods in reducing the risk of subsequent treatment failures.