MONEY MARKETS-U.S. swap spread narrows on record low Libor

* Rock-bottom Libor narrows U.S. 2-year swap spread

* Two-year swap spread tightest since June 2007

* U.S. commercial paper market smallest in over 4 years (Updates with CP data, changes dateline, previous London)

By Richard Leong and Ian Chua

NEW YORK/LONDON, May 7 (Reuters) - The cost to exchange two-year fixed-rate dollars for floating-rate fell on Thursday to its lowest level in about two years as a key interbank rate hit record low for a third consecutive day.

A further drop in this gauge of corporate debt expense signals the continued healing of credit markets since the peak of the credit crisis last autumn.

The spread or risk premium on two-year dollar interest rate swaps shrank to 44.75 basis points, the lowest since early June 2007, from 46.25 basis points late Wednesday.

Last September, two-year swap spread approached 160 basis points, as credit markets were nearly frozen in the wake of the collapse of Lehman Brothers.

Analysts cautioned borrowing costs are still running well above their long-term historical averages as many companies remained fearful of a prolonged global downturn. They have been paring their short-term borrowing in addition to inventories and payrolls, analysts said.