Approximately 12 percent of Seattle homes and 20 percent of local condominiums remained mired in negative equity in the second quarter of 2015, according to the Zillow Negative Equity Report.

Overall, the Seattle market improved significantly from the second quarter of last year. The percentage of homes that had been in a negative equity position was reduced by 34.2 percent.

According to Zillow, the continued decline of the overall negative equity rate was fueled in the first half of the year by strong appreciation for the least valuable third of homes. The least valuable homes are much more likely to be underwater than more valuable homes.

“If the overall negative equity rate is going to continue to fall, it will need to keep being driven down by improving health at the bottom end of the market,” said Svenja Gudell, Zillow’s chief economist. “The least valuable homes really bore the brunt of negative equity during the recession, and that’s where most negative equity remains concentrated today. . .”

Seattle’s condo negative equity equaled the national average while its overall rate of 12 was three percentage points below the national number of 15.