Two trouble spots in the economy showed little sign of improvement in the last few months, as home prices fell again in May and consumer confidence stagnated in July, according to a pair of reports out Tuesday.

    Home prices, already falling at the steepest rate in two decades, tumbled again in May, according to the Case-Shiller index, a widely watched survey that measures prices in 20 major metropolitan areas.

    Prices were down 15.8 percent from May 2007, including a 0.9 percent one-month drop in May alone. The 10-city price index, which dates to 1988, dropped 16.9 percent, its sharpest decline on record.

    All 20 cities measured by the index showed annual declines in home values, and 10 cities have suffered double-digit percentage declines in the last year. Miami and Las Vegas have fared the worst, with prices in each city dropping more than 28 percent since May 2007.

    There were some signs that the decline has started to abate. Prices in seven regions, including Boston, Dallas and Charlotte, improved in May, some for the second straight month. Boston, for example, was up 1.05 percent in May, though values are still 6.2 percent below where they were a year prior.

    The report "does seem to suggest the rate of decline of existing home prices is slowing," Ian Shepherdson of High Frequency Economics wrote in a note. "To be sure, prices are still falling very rapidly, and there is no prospect of any rebound this year and probably next, but a slower rate of fall is welcome nonetheless."

    Las Vegas, Miami and Phoenix had the sharpest declines in May, with Miami losing 3.6 percent. The city recorded a 28.3 percent price drop for the last 12 months.

    Another month of falling home values may continue to put pressure on investors who are concerned the housing crisis is fueling the credit problems on Wall Street. Last week, a dip in sales of newly built homes helped lead to a sharp decline in the stock market.

    In a separate report on Tuesday, the Conference Board, a private research group, said that Americans remained unhappy about the state of their economy in July, though their confidence did not change markedly from a month prior.

    The group's consumer confidence index rose to 51.9 from 51 in June, and a measure of expectations about the economy's prospects rose to 43 from 41.4. Those figures are historically very low.

    "It is not a particularly good sign that consumer confidence and sentiment levels remain as low as they are, even after almost $100 billion of tax rebates have hit consumer's wallets in the past several months," Joshua Shapiro, the chief domestic economic at MFR, said in a note.

    The Conference Board sends its questionnaire to 5,000 households.