The Department for Energy and Climate Change (Decc) announced the change in a decision document published this week, which also sets out new rules on unincorporated joint ventures (UJVs).
Generators will no longer be due payments under a CfD when the day-ahead electricity market price is negative for more than six hours. This is known as negative pricing.
While this has never happened in the UK to date, it has in other countries when renewable energy deployment is high and consumer demand is low.
The plans were initially laid out in a government consultation in April, but Decc admits that most respondents "disagreed with the proposals in principle".
Critics feared that voiding CfD payments under prolonged negative pricing is contrary to the general principle of a subsidy that aims to attract investment by reducing wholesale market price risk.
Some said the changes would bring more uncertainty for investors, because they would open CfDs up to unpredictable market events. "A small number of respondents expressed concern that [the proposals] may impact the bankability of the CfD," Decc said.
In its response, industry trade association Energy UK warned that the move "fundamentally changes the aim of the CfD".
While not going so far as to say that they undermine the essential function of the CfD, Energy UK's senior policy manager for generation, Pavel Miller, said: "The changes significantly alter the CfD proposition by presenting a new set of risks to investors around negative day-ahead market prices which they will need to take a view on over the lifetime of the project."
Decc is making the changes to comply with updated state aid guidelines from the European Commission, which must be in place by 2016.
These aim to ensure that subsidy mechanisms do not buffer an industry's response to market signals.
If negative pricing happens, the signal to industry should be to stop generating electricity. The knock-on environmental implication would be that over-generation is also halted.
But CfDs in their current guise may be seen to nullify this signal through their payment guarantee.
In an attempt to appease detractors, Decc has also published an independent report on future likelihood of negative pricing by consultancy Baringa. This models two future market scenarios and finds the likelihood of negative pricing is rare in both.
Decc noted that alternative ways of complying with state aid guidelines had been explored by a CfD expert group in late 2014. It gives no reason why this particular approach was chosen, but says it will continue to engage with the European Commission and industry on future alternatives.
As well as negative pricing, the consultation confirms the much less controversial decision to allow UJVs to bid for CfDs in future.
The amendments will be laid before parliament in the coming months and will be included in the next version of the CfD contract.