You really need to know your market value, research as much as possible natioanl and regional salaries and accurately estimate your experience and skill level. Stating slightly higher figures than average is a sign to the employer that you have confidence in your ability and value to the company, plus sets a higher starting point for negotions.
It is rare for a company to somehow withdraw an offer because your requested salary was too high unless you are unwilling to negotiate to reasonable salaries.
Anyway nice companies to work for will usually pay more than the regional average and be happy with paying employers what they are happy with. The difference between x thousand and 1.2*x is to that high. You have to realise that your total cost to the company is far higher than the salary alone, typically 3-5x your annual salary is your annual company cost when all extras and fixed charges are included. Increasing the saLary by 10-20% doesn't change their running cost much. The excepts are for complete entry level unskilled.
Saying that my last salary negotions was non existent, I did as much research as I could and found the top figure, add 15% to start negotions and was offer 20% more on top of what I asked, I had then no space to negotiate and I thought the salary more than fair and plenty to live by so I simply agreed.
You also have some power to negotiate salaries after 6-12 months reviews. In many jobs the ramp up periods means for the first years or so you are o where near fully productive, there is a training or learning period, the first months you might be barely functional. Hence once this period is over and you can demonstrate your added value you can negotiate a raise. You have some power because if you quit because they don't meet your demands then the. Company looses out on their investment in taking you on.