TeV gamma-ray signals from the Crab Nebula and Mkn 501 were detected with the HEGRA CT1 imaging Cerenkov telescope during periods when the moon was shining and during twilight. This was accomplished by lowering the high voltage supply of the photomultipliers in fixed steps up to 13%. No other adjustments were made and no filters were used. Laser runs could not establish any nonlinearity in the gain of the individual pixels, and the trigger rate was uniform over the whole camera. The energy threshold was increased by up to a factor of two, depending on the amount of HV reduction. In a series of observations lasting 11.7 hours, a signal with a 3.4sigma significance was detected from the Crab. During the 1997 multiple flare episode of Mkn 501 a 26sigma combined excess was recorded during 134 hours of observations under various moonshine/twilight conditions. The results show that this technique can easily be adapted to increase the exposure of a source, which is important for sources showing rapid time variability such as AGNs or GRBs. Observations can be made up to ~20^∘ angular separation from the moon and until the moon is 85% illuminated (ten to eleven days before and after new moon), as well as during 20 to 40 minutes during twilight, before the commencement of astronomical darkness.