The idea when flying a DME arc is, first, to stay within two miles, and preferrably second not to fly the arc with either a constant angle of bank, or many small angles.
Why not? Because a constant angle of bank will eventually cause the artificial horizon to re-erect in the turn, causing an error than will be a problem later. The artificial horizon is self-erecting, and in the turn the horizon will "erect" in the turn (as a balanced turn results in the total force being experienced through the floor of the aircraft, regardless of bank.)
How to avoid this? With an ADF needle, once you have turned onto the arc set the needle about 10° forward of the wing, then hold the aircraft level until the needle is 10° aft of the wing, then turn 20° and continue.
With a VOR display you do the same thing. Set the OBS to the initial radial you are on (ie centre the needle) then fly level until the needle is at full deflection (10° off the radial), turn the OBS 20° (ie swing the needle to the other side of the display) and fly level until the needle has crossed for that side of the display to the other side, and adjust the OBS another 20° etc.