The lower rate has been possible to arrange, brokers said, by agreeing to take some older and less fuel-efficient vessels for up to 12 months.
"In 2009 freight rates were extremely low and owners were willing to put their ships out on charter in order to mitigate weak spot rates," said Christian Waldegrave at leading tanker owner Teekay.
"In a rising freight market, such as we are in now, I would think that owners would be more hesitant to fix out their ships on time charter unless they felt strongly that rates were about to decline."
Initial indications are around 12-15 million barrels of floating storage have been booked so far. In 2009 at least 100 million barrels of oil ended up being stored at sea.
Shipping sources said more oil traders have also been making enquiries in the past week.
Analysts at JBC Energy in Vienna said floating storage, while a sign of an oversupplied market, may provide some temporary support for oil prices in the coming weeks now that traders were able to move crude on to tankers.
"This will not only release some pressure on front-end prices, but also allow for the physical market to clear somewhat," JBC Energy said in a note.
"The physical market could also turn temporarily supportive over the coming months thanks to the balancing effect of floating storage."