A low fare ticket option with Finnair caught my eye today at $364 round trip for New York JFK to Copenhagen via Helsinki for flights from mid-August to end of schedule March 2018. This ticket might allow scheduling overnight transit layovers in Helsinki.
In a rare occurrence, fares found on Google Flights ($364) are lower than seen on Momondo.com ($410) for dates I checked.
American Airlines (Finnair operate flights)
New York JFK – Helsinki HEL – Copenhagen CPH – HEL – JFK