A passer-by on Sunday discovered a first suitcase containing human remains bobbing in the Traun lake in western Austria, and a police dog then later found a second one.
Police divers later found a third bag containing her head encased in concrete, as well as the body of a man. The suitcase remains were identified as those of a woman aged around 70.
The man, whose body was found in around five metres (15 feet) of water, had two bags attached to his wrists containing "commercially available granite stones" and "personal tools", Austrian police said.
Autopsies suggested that the woman was strangled between December 25th and January 1st, and that the man drowned some time later. There was no indication of involvement of a third party.
The two suitcases were found close to Gschliefgrabens. Photo: salzi.at
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"We believe first and foremost that (the man's death) was suicide," state prosecutor Birgit Ahamer told a news conference.
The man and woman were later identified as a couple in their 70s from near Frankfurt in western Germany.