LONDON — It was less than three years ago that Scotland's bid for independence fizzled, with a much-hyped referendum failing by 10 points and Scotland's pro-independence party left embarrassed.

But the drive for self-determination in Scotland is as strong as ever. On Tuesday, the Scottish parliament backed First Minister Nicola Sturgeon's attempt to seek another independence vote. And, much to the dismay of officials in Madrid, Copenhagen, Brussels and other capitals, breakaway attempts in other countries are also alive and well.

To some, this is yet another indication that the European Union is falling apart and unable to keep the divided continent united. But in reality, Europe's powerful independence movements are a sign of European strength, not discord.

The three regions where independence votes are now most likely — Catalonia, Scotland and the Faroe Islands (which is not part of the E.U.) — are doing so in an attempt to assume a more active role on the international stage and in the European Union. All three regions argue that independence would put them in a better position to interact with the union, both economically and politically.

The Faroe Islands, a Danish-controlled autonomous territory in the North Atlantic, announced in February that it will vote on a new constitution next year, most likely paving the way for an independence referendum there.

On the Faroe Islands, pro-E.U. sentiments are mainly driven by economic considerations. Due to its dependency on the E.U. as a trading partner, the Faroe Islands wants to renegotiate relations with the bloc — something its association with the Kingdom of Denmark has so far largely prevented because the Faroe Islands do not handle their foreign affairs themselves.

Farther south, the region of Catalonia, home to Barcelona, has long sought independence from Spain. Its distinct traditions and language, Catalan, have driven such hopes for decades — but there is also a political rationale behind the desire to break away from Spain. Catalonia already has a foreign affairs commissioner, and its citizens are some of the E.U.'s most loyal supporters. As many as 200,000 people recently marched in Barcelona urging the Spanish government to accommodate more refugees and meet the E.U. criteria that are being virtually ignored by almost every member state.

Previous demonstrations in favor of independence deliberately included the word “Europe” in their slogans (“Catalonia, a new state in Europe”) and the current regional leader, Carles Puigdemont, is staunchly pro-European. Puigdemont and his political allies hope that independence from Spain would allow Catalonia, which has more inhabitants than Denmark, to finally influence European affairs without having to take a detour through Madrid.

In the case of Scotland, preserving E.U. membership is also one of the biggest driving forces behind the new independence campaign. Keeping E.U. membership was among the key reasons the Scottish voted against independence in 2014. Ahead of the vote, officials in London had warned that Scotland would also have to leave the E.U. if it decided to leave the United Kingdom.

That argument became void in June last year when Britain decided to leave the E.U., anyway. Scotland, however, voted against leaving the European Union by a margin of 24 percentage points, which political leaders there say proves that a new independence vote is needed.

Of course, things are unlikely to be as easy as pro-independence politicians are saying. The E.U. has said that an independent Scotland would have to apply for admission to the union as a new state, meaning a likely delay of several years. That could complicate the case for a breakaway.

Nor is it certain the E.U. would approve membership. Whereas Britain is leaving the union and would be unlikely to veto an application by Scotland, other countries might be more willing to take such measures. In 2014, Belgium and Spain said they would veto a Scottish membership application in an attempt to prevent other independence movements in Europe from gaining momentum.

Apart from such legal and political obstacles, there is also the question whether voters would even want their regions or nations to become fully independent. Recent opinion polls in Catalonia and Scotland do not show a clear majority.

Pro-independence activists, however, say that voters should at least have a chance to decide. They hope that support for separation might rise if the referendum plans themselves are being blocked by national authorities.

The Spanish government has already declared a possible referendum illegal and said it will not recognize the results, but popular support for such a referendum is still on the rise. Meanwhile, in Britain, Prime Minister Theresa May has indicated that another independence vote won't happen anytime soon — which may only stoke the desire for Scotland to go its own way.