The maximum drawdown control strategy dynamically allocates wealth between cash and a risky portfolio, keeping losses below a chosen pre-defined level. This paper introduces variations of the strategy, namely the excess drawdown and the relative drawdown control strategies. The excess drawdown control is a more flexible strategy that can cope with common (re)allocation restrictions such as lock-up periods, cash bans or liquidity constraints through an implementation with a hedging overlay. The relative drawdown control strategy is adapted to contexts in which investors seek to limit benchmark underperformance instead of absolute losses. A formal proof that the loss-control objectives introduced can be insured using dynamic allocation is provided and the potential benefits and implementation aspects of the strategies are illustrated with examples.