In its 2017 revision of the global guidelines for HIV care and treatment, the World Health Organization called for rapid or same-day initiation of antiretroviral treatment (ART) for eligible patients testing positive for HIV. In sub-Saharan Africa, where most HIV patients are located, studies continue to document high losses of treatment-eligible patients from care before they receive their first dose of antiretroviral medications (ARVs). Among facility-level reasons for these losses are treatment initiation protocols that require multiple clinic visits and long waiting times before a patient who tests positive for HIV is dispensed an initial supply of medications. Simpler, more efficient, accelerated algorithms for ART initiation are needed, including strategies for rapid initiation in patients with symptoms of tuberculosis, most of whom do not have active TB.