In my opinion gengejbee is correct, putting something on top of a bad mattress is a waste of effort and money. I understand that the medical profession advises a mattress that remains flat and firm to avoid back pain. We (70-ish) sleep on mattresses which are extremely firm and neither of us has ever had back pain. Visitors from Australia recently used these and remarked that they slept extremely well with one of them particularly mentioning that the joint pains that normally come with waking up simply were not there. Another couple recently asked me what it was about our bed that led to them sleeping so well on it...... when they visited us in 2010 !
The bed has a plywood base which does not give at all and the mattress is 7cm thick of a material sometimes called upholstery foam (made up of shredded foams of many different types, then glued back into a block) and has very limited give. Oddly enough, advertisers of mattresses tend to emphasise the large number and types of springs, the overall thickness of the mattress (is it meant to give by as much as 40cm or more ?) and its ability to be shaped (and also beds that can be be bent into a variety of shapes, including that of a hammock). Presumably the medics regard these as creators of back problems.