In 2017 Denmark was named the second best country for gender equality in the European Union, beaten only by its neighbour Sweden.
It was one of only nine countries to hit EU childcare targets, had one of the most gender-equal attitudes to housework, and was one of the few European countries close to achieving a 50:50 parliament, according to the Gender Equality Index.
But in a report released last week, Amnesty International warned that Denmark also has "widespread sexual violence" and systemic problems in how it deals with rape.
Several studies say that Denmark has the highest prevalence of sexual violence in Europe.
The Danish Ministry of Justice estimates that around 5,100 women a year are victims of rape or attempted rape, while the University of Southern Denmark put this figure as high as 24,000 in 2017 - a high number for a country with a relatively small population (5.8 million).
That same year, only 890 rapes were reported to the police, of which 535 led to prosecutions, and 94 ended in convictions.
Speaking to Amnesty, victims said they often found "the reporting process and its aftermath immensely traumatising", either because they were not believed, they were interrogated by officers, or, in one case, important evidence that was later needed at trial was allegedly not properly collected.
The National Danish Police have told BBC News that they are striving to improve how they deal with people reporting rape, and that they are working to new guidelines that were drawn up in 2016.
So how did a country with an otherwise impressive record of gender equality end up being named one of the worst on the continent for violence against women?
'A hindrance to equality'
Some believe the Scandinavian country's image as a progressive utopia has actually added to the problem.
"We have this general notion that we have already achieved gender equality in Denmark, that the fight is over and there's nothing left to fight for," Helena Gleesborg Hansen, vice president of the Danish Women's Society, tells BBC News. "And this is the biggest hindrance we see when we talk about gender equality."
Denmark was one of the first countries to sign up to the Council of Europe Convention on Preventing and Combating Violence Against Women and Domestic Violence (the Istanbul Convention) - a wide-ranging international treaty that seeks to combat violence against women worldwide.
But despite Denmark getting on board early, Grevio, the group set up to monitor whether countries are correctly implementing the convention, warned that it was still falling short in 2017.
One fundamental issue, the group said, was the definition of rape in Danish law.
Is the law victim-blaming?
Crucially, it defines rape as involving force or a threat of violence, rather than on whether or not there was consent.
For this reason, the Danish National Police Guidelines say that officers should ask rape complainants about "resistance to the perpetrator" - that is, whether or not they tried to physically fight them off.
But consent, Grevio said in its report, "is the central element in the way the Istanbul Convention frames sexual violence".
Ms Hansen says the current law puts the onus on the victim to stop themselves being raped, rather than on the perpetrator to not commit the act - which in turn leads to a pervasive victim-blaming attitude.
"We have all these myths around rape", including that rapists are often "monster attackers" who jump out of bushes to assault women as they walk alone, she says.
However, "most rapes that happen are actually [committed by the victim's] husband, boyfriend, best friend, someone they met at a party. In these cases, there's a shift of the guilt onto the victim, because they know each other. Which is what I find strange, because rape and sexual assault are never the victim's fault - never."
Focusing on whether or not there was a physical struggle, she adds, shows a lack of understanding of what can happen to a person when they are raped.
"A lot of people in these situations freeze, or get very confused - or they may be asleep, or drunk, or sedated," she explains. "In the law right now, your body is accessible until you say 'no' and fight back. But we'd rather have it so your body is not accessible until you say 'yes'."
What about the rest of Europe?
Denmark isn't the only European country to have drawn criticism for having a force-based definition of rape.
According to another recent report from Amnesty released in November, out of 31 European countries they looked into, only eight have consent-based definitions of rape.
Of those, Germany only changed to a consent-based definition in 2016. Victims also used to have to prove that they physically resisted their rapists, but this was repealed that year too.
And Sweden, Denmark's neighbour and the top country in the EU's Gender Equality Index, only brought in a consent-based law last July.
Spain has yet to change its rape laws, but it's in the process of doing so now. Under its current law a complainant needs to prove there was violence or intimidation in order for their case to be treated as a "rape".
Last year, this led to a gang of men who attacked an 18-year-old woman getting acquitted of gang rape - which in turn prompted a panel of legal experts to recommend the law be tightened to define any non-consensual sexual act as "assault" or "rape".
In some respects, Denmark is ahead of other countries on the continent. Along with Norway, Sweden and Finland, rape complainants have access to free legal representation.
A lack of trust in the system
Activists say that certain minority groups may find it particularly hard to get help.
Nico Miskow Friborg, from the group TransAktion, tells BBC News that "generally, there's a lack of trust in the system among trans people, because of transphobia in different corners of the system - if they've had experience of police harassment, for example, or experience of transphobia and discrimination in the healthcare system."
They add that many of the services set up to support people who have experienced violence - such as rape clinics and counselling - are either explicitly or implicitly promoted towards cisgender women, which can also alienate trans people in need.
Amnesty also points out that Danish police don't record whether a rape complainant is cisgender, transgender or non-binary - only that they're either male or female. This means campaigners like Nico can't track how many trans people are affected, and how many of those are targeted specifically because they are trans.
Bwalya Sørensen, a founder of Black Lives Matter Denmark, adds that migrant spouses are particularly vulnerable, because their abusers tell them police won't investigate a rape where the rapist and the victim know each other. Denmark only fully criminalised spousal rape in 2013.
"These are people they are married to or have children with who are doing this," she explains, adding that Denmark's tough immigration requirements mean that abusers with migrant partners "know the women can't escape".
"They know the police will not listen to her, they'll listen to him," she adds.
What do the Danish authorities say?
In response, the Danish National Police say they are committed to addressing the issues raised, and that they will "of course take the criticism from Amnesty into consideration".
"Victims of sexual assault are in an extremely vulnerable situation, [which is] why the Danish police are focused on meeting the victims in a respectful and sensitive manner," a spokesman told BBC News.
"In 2016 we initiated a large co-operation with other Danish authorities aiming at further strengthening our work when it comes to cases of sexual assault."
One of the things they've been working on, he said, is improving the way victims are dealt with when they first file a report - an effort that "continues to be in progress".
"Fortunately, the number of victims unhappy with the police [saw] a decline from 30% to 15% in 2018," he added. "This indicates that our new guidelines and initiatives have made a difference for the victims. But 15% is still 15% too many."
Meanwhile, Denmark's Justice Minister Søren Pape Poulsen has told local media he also supports the call for improved legislation based on consent.