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A street around the corner from me in Frederiksberg is being converted from painted bike lanes to separated bike lanes, with a kerb/curb. I ride on this stretch almost every day and I’ve never felt like the stretch needed a physically separated lane, but I’m certainly pleased it is soon finished.
In the new suburb of Ørestad - as with all new development - building bike lanes is a requirement. There are also separated lanes along the main road through the suburb, but here you also get a quieter route if you wish to use it.