We develop the theory of operation for dispersive spectrometers that modulate radiation at both the entrance and exit apertures by means of Hadamard codes. Specifically, we examine the operation of instruments illuminated by a beam of radiation known to be homogeneous. In this case, all spatial information obtained in the operation of the instrument can be effectively suppressed at no loss of spectral performance and at a considerable reduction in the number of measurements that need to be made. A particularly interesting instrument which mocks a monochromator is described. The spectrum is directly obtained from the data by simply subtracting a constant intensity value from all readings. This instrument bears a resemblance to the Girard grill spectrometer. We describe the construction and operation of an instrument that has been tested in both modes of operation and show some of the spectra obtained.