Qualified Principal Residence Indebtedness
You can exclude canceled debt from income if it is qualified principal residence indebtedness. Qualified principal residence indebtedness is any mortgage you took out to buy, build, or substantially improve your main home. It also must be secured by your main home. Qualified principal residence indebtedness also includes any debt secured by your main home that you used to refinance a mortgage you took out to buy, build, or substantially improve your main home, but only up to the amount of the old mortgage principal just before the refinancing.
The above is a copy/paste from the horses mouth. IRS Publication 4681 published in 2010 as quoted above answers your question as follows: The debt forgiveness on the 10% second mortgage will not be taxable income to you (neither would the forgiveness from the first mortgage, but, as you've probably already learned, getting forgiveness on the first is definitely a horse of a different color!)