Quantum-well infrared photodetectors (QWIPs) are trapping-mode photodetectors, and it is trapping that leads to an inherent problem: QWIPs' responsivity can be background-dependent under low-background conditions. We have determined that the source of the dependence is a relaxation process due solely to dielectric effects (dielectric relaxation), which results in a long time constant for recovery to steady state after a pulse of radiation is detected. We have analyzed responsivity-versus-frequency measurements on QWIPs published separately by Arrington et al. We have determined the value of the background flux for which significant background dependence occurs. For a given sensor integration time τi (frame time for a staring sensor, dwell time for a scanning sensor), we calculated the response as a function of an exponential time constant. Fitting the calculated response to the measured data, we extracted values for the exponential time constant. We then determined the lower bound of background flux, ΦBL, above which the total responsivity will be less than 1% background-dependent. The value of ΦBL for a typical QWIP detector is such that ΦBLτi lies between 1012 and 1013 photons cm–2. Practically, when significant background dependence occurs, it is essentially impossible to calibrate a QWIP-based focal plane array. And this, together with their the inherently low sensitivity and low required operating temperature (compared with HgCdTe detectors), makes QWIPs a poor choice for many low-background spaceborne sensors.