Measurements of the strengths of the diffuse interstellar bands at 4430, 5780 and 5797 A show that the bands tend to be weak with respect to extinction in dense interstellar clouds. Data on 10 stars in the Q Ophiuchi cloud complex show further that the diffuse band-producing efficiency of the grains decreases systematically with increasing grain size. It is concluded that the diffuse bands are not formed in the mantles which accrete on the grains in interstellar clouds, but that they could be produced in the cores of grains or in some molecular species.