We've flown the MS5611-01BA03 with good success. It is specified down to 10mb. Even without setting the local barometric pressure, it is generally within 100 Ft of actual altitude at launch. At birst altitude, it can be off by a thousand feet or more.
Be sure you factor in temperature and the factory calibration data. The data sheet does a good job of explaining the steps to get to temperature compensated barometric pressure with modifications for low temperature. Watch out for the the size of the resultant math. They specify 32 and 64 bit integer math which can introduce errors if not done right.
There is one equation for calculating altitude at launch, and another for high altitudes. I don't recall what the second equation is or what altitude it kicks in at off the top of my head. I think it is around 36K feet..
I hope this helps.
Mark - KC0D