The time it will take to complete a project is fixed but unknowable. The only thing you can control is the scope and the cost for each unit of work. Therefore the only strategy is to do the least amount of work you can possibly do for the least possible cost. If someone requires you to fix your costs you have to charge them a lot more money. Best to tell them that whatever happens, nothing could have been done to improve it and make sure they're willing to compromise heavily to get it live.