Quasi-static speckles are a current limitation to faint companion imaging of bright stars. Here we show through simulation and theory that an adaptive pupil mask can be used to reduce these speckles and increase the visibility of faint companions. This is achieved by placing an adaptive mask in the conjugate pupil plane of the telescope. The mask consists of a number of independently controllable elements which can either allow the light in the subaperture to pass or block it. This actively changes the shape of the telescope pupil and hence the diffraction pattern in the focal plane. By randomly blocking subapertures, we force the quasi-static speckles to become dynamic. The long-exposure point spread function (PSF) is then smooth, absent of quasi-static speckles. However, as the PSF will now contain a larger halo due to the blocking, the signal-to-noise ratio (SNR) is reduced requiring longer exposure times to detect the companion. For example, in the specific case of a faint companion at 5λ/D, the exposure time to achieve the same SNR will be increased by a factor of 1.35. In addition, we show that the visibility of companions can be greatly enhanced in comparison to long exposures, when the dark speckle method is applied to short-exposure images taken with the adaptive pupil mask. We show that the contrast ratio between the PSF peak and the halo is then increased by a factor of approximately 100 (5 mag), and we detect companions 11 mag fainter than the star at 5λ/D and up to 18 mag fainter at 22.5λ/D.