Dustmen discovered a woman's body wrapped in an old duvet.
They were about to toss the quilt into their dustcart while on their rounds close to Brighton seafront.
Paramedics were called to the landing of stairs outside the former Bedford Hotel, now the Hilton West Pier, in Cavendish Place.
It was thought the 20-year-old died from a suspected drugs overdose but tests were continuing.
Detective Inspector Graham Pratt, heading the inquiry, said police believed the woman died elsewhere and the body was moved to the stairs.
Her identity was being withheld until a formal identification had been carried out.
Her family was expected to travel to Brighton tomorrow.
Anyone with information should contact Brighton and Hove CID on 0845 6070999.
The woman, who was found on Monday, was the second person to die from suspected drug overdoses in the city this week.
Last night, a 24-year-old man was discovered at a flat in Fourth Avenue, Hove.
A friend found the body and called an ambulance.
The dead man was believed to be local.
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