The confluence of high-temperature (1600-3200 K) flameless combustion chambers and vertical junction (VJ) photovoltaics creates the possibility of ultra-compact high-efficiency thermophotovoltaic (TPV) generators. The actively-cooled cells can be sited at the chamber's aperture without contaminating or damaging them. The flux density, however, is then well above values at which conventional TPV cells can operate efficiently due to the series resistance losses at photo-generated current densities of the order of tens to hundreds of A/cm(2). Generally, this problem is resolved by distancing the cells from the radiator, but at the price of dramatically increasing the requisite cell area and system size. VJ cells offer an intrinsically low-current low-series-resistance configuration that obviates the problem. But carrier dynamics then mandate that only indirect-bandgap semiconductors can provide practical solutions. Silicon and Germanium are the candidates analyzed here, with simulated performance rivaling or exceeding current TPV generators. We also evaluate the degree to which efficiency can be increased by introducing a cell back-surface mirror that recirculates sub-bandgap photons back to the combustion region. The unobvious energetic advantage of recirculating photons by (1) increasing combustion chamber temperature at fixed fuel consumption rate, vs. (2) reducing fuel consumption rate at fixed combustion chamber temperature is also evaluated. (C) 2016 Elsevier B.V. All rights reserved.