Solving for a camera's sensors based on its response to the surfaces of a calibration target is an ill-conditioned problem with an infinite number of possible solutions. To obtain a stable estimate we need to control the solution space by constraining the sensors to match some known physical characteristics e.g. sensors are normally constrained to be positive. The use of constraints limits the uncertainty encountered in sensor recovery and results in improved estimates. Unfortunately, it is not possible to know which exact constraints should be used in recovering an unknown sensor. In this paper we present a method to estimate the support (the region where the sensor's sensitivity is not zero) of a sensor prior to recovering it. If the sensor's support is limited this constraint is very stringent and imposing it on the solution space results in a clear reduction in the uncertainty encountered in the solution. In the results section we show that it is indeed possible to recover a sensor's bandwidth based on its response to a set of reflectances.