Background coming from the Formula omittedAr decay chain is considered to be one of the most relevant for the Gerda experiment, which searches for the neutrinoless double beta decay of Formula omittedGe. The sensitivity strongly relies on the absence of background around the Q-value of the decay. Background coming from Formula omittedK, a progeny of Formula omittedAr, can contribute to that background via electrons from the continuous spectrum with an endpoint at 3.5 MeV. Research and development on the suppression methods targeting this source of background were performed at the low-background test facility LArGe . It was demonstrated that by reducing Formula omittedK ion collection on the surfaces of the broad energy germanium detectors in combination with pulse shape discrimination techniques and an argon scintillation veto, it is possible to suppress Formula omittedK background by three orders of magnitude. This is sufficient for Phase II of the Gerda experiment.