There are portfolio products that you may be able to find with no pmi and a low downpayment. However, you typically will pay a higher interest rate in lieu of the PMI.
PMI is tax deductible and only stays on the property for an average of 7 years...
Downpayment of approx. 20% - or + will eliminate a PMI charges
Confer with mortgage broker review all financial obligations for term of loan for 3.5% down with PMI and larger downpayment no PMI.