There are really two issues in play here:
1) The length of time that one is self-employed.
2) Qualifying the income, if possible, from that employment.
As long as there is a self-employment history, you can do a 1-year tax return application for a conforming loan so long as your lender can get automated underwriting system (AUS) findings from Fannie Mae or Freddie Mac that say you can do this. On the Freddie side (FHLMC), which is how most lenders try to do this, there was a recent change that requires that you must have been self-employed for at least 5 years, otherwise 2 years of returns will be required. Note that in every case here, it's generally not possible to get a loan if a borrower has only been self-employed for one year. Lenders view this as not enough history to make a strong determination on income stability. FHA will require two years of self-employment and tax returns as well.
On the jumbo side of things, should anyone be reading this response and have a loan amount that falls above the conforming limits, we can do a 1-year tax return qualification up to a loan amount of $2MM with a maximum loan-to-value (LTV) of 80% and a minimum FICO of 660. We can go to a maximum loan amount of $3.5MM on this program, but there only to an LTV of 60.
Long story short, if you're self-employed and need to work off only your most recent year's taxes, get in touch and we'll make our best effort to help. Thank you!