The government is to consider putting extra pressure on computer users to filter out pornography when setting up internet accounts.
Ministers are suggesting that people should automatically be barred from accessing unsuitable adult material unless they actually choose to view it.
It is one of several suggestions being put out for a consultation on how to shield children from pornography.
Websites promoting suicide, anorexia and self-harm are also being targeted.
The discussion paper asks for views on three broad options for the best approach to keeping children safe online, in a rapidly changing digital industry.
Conservative MP Claire Perry has pushed for restrictions to go further, so that each internet service provider automatically blocks "harmful content" and users have to contact the company to reverse this.
The government has already proposed a system called "active choice", where new customers are asked whether they want open access to all content.
Code of practice
The latest system, called "active choice-plus", is aimed at reaching a compromise.
It would automatically block adult content, but would set users a question, along the lines of whether they want to change this to gain access to sites promoting pornography, violence and other adult-only themes.
This is partly based on "Nudge" theory, a US concept which states that persuasion, rather than enforcement, can be an effective way of changing behaviour. Downing Street has set up a unit to explore such ideas.
The four main internet service providers - BT, TalkTalk, Virgin Media and Sky - have signed up to a code of practice, offering customers a choice of whether to apply filters.
Yet ministers acknowledge that such technology is not 100% effective. The government's consultation will look at which system can best protect young people.
Children's minister Tim Loughton said: "The internet is transforming every aspect of society and family life - and opens up enormous opportunities for us all. But with the benefits come risks. Growing numbers of parents do not feel in control of what their families are exposed to online.
"Many want to take responsibility, but all too often they do not how know how because they find the technology too difficult to use or their children are more technically advanced then they are."
He added: "There is no silver bullet to solve this. No filter can ever be 100% foolproof. There is a cottage industry of people, mostly operating outside the UK, continually creating and proliferating 'proxy' websites that provide links to adult and harmful content.
"Automatic filtering on its own risks lulling parents into a false sense of security and there can never be any substitute for parents taking responsibility for how, when and where their children use the internet. The answer lies in finding ways to combine technical solutions with better education, information and, if necessary regulation further down the line."
In an earlier statement, Prime Minister David Cameron said: "I want to fully explore every option that might help make children safer - including whether internet filters should be switched on as the default, so that adult content is blocked unless you decide otherwise."