Well, if the offer comes in around your previous salary you can ask for more or a signing bonus to get you where you want. Otherwise, you need leverage. Without an equal opportunity otherwise, sometimes you just have to say No to the offer, if it is not competitive and keep on interviewing. They may come back later and give you what you want. However, this strategy should be balanced against the 20k you have and how far and how many interviews you've had. Expect rejection and give yourself 1-2 months.
Also, always make your own coffee and if not possible, buy drip coffee.