* Italian debt rallies across curve ahead of T-bill sale * Strong domestic demand for 6-month debt, boosted by ECB cash * Sterner test to come at Thursday's 3-, 10-year debt auctions By William James LONDON, Dec 28 (Reuters) - Italian bond yields fell and investors bought up the country's short-term debt on Wednesday in the first sign that an injection of ECB cash could ease funding pressure, although sterner tests were due later this week. Italy sold 9 billion euros of six month debt at a yield of 3.25 percent - just half the euro-era record high yield it had to pay in November. T-bill auctions usually benefit from the support of domestic banks, some of which borrowed heavily at the European Central Bank's offer of cheap three-year loans last week. This extra cash was one factor boosting demand, analysts said. "The ECB's new liquidity measures have clearly helped and today's sale augurs well for tomorrow's more challenging auction of longer-term paper," said Nicholas Spiro, managing director at Spiro Sovereign Strategy. Italian bonds rallied ahead of the sale, reversing an earlier fall. The two-year benchmark yield fell 11 basis points on the day to 5.084 percent while 10-year bonds yielded 18 bps less at 6.8 percent. Traders cautioned that buying volumes on the papers were very low, with volatile price moves seen likely ahead of Thursday's trickier sales of long-term debt. While 10-year yields remain within sight of the 7 percent level that has downed other victims of the euro zone's debt crisis, Italy faces a tough task to convince long-term investors it can continue refinancing debt at affordable levels. As a result, broader market sentiment was likely to remain fragile ahead of Thursday's 8.5 billion euro sale of three and 10-year bonds, with some fearing weak demand from an increasingly scarce pool of willing international investors. "The uncertainty surrounding the Italian auctions remains high as several European banks recently have made a point of (publicising) the large reductions in their exposures to Italian and Spanish government debt," said SEB strategists in a note. "Hence it seems unlikely that banks outside Italy will show any meaningful interest in the upcoming auctions." Bund futures traded 11 ticks lower on the day at 137.87, with extremely low liquidity fuelling volatile price movements. Ten-year German bond yields were 1.2 basis points higher at 1.935 percent.

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