The anti-HIV p24 immune response resulting from Vacc-4x immunization could in combination with ART potentially improve immune reconstitution in patients who have not fully regained a healthy CD4 level (> 600 x106/L). Adding the immunomodulatory agent Lenalidomide (CC-5013) to Vacc-4x immunization could enhance the immune response to Vacc-4x and further strengthen immune reconstitution.