Those convicted of offences would have points deducted from them to make it harder for them to get one of Anglesey's 5,000 council homes.
The plan drew criticism from Shelter, but Anglesey housing director John Arthur Jones is determined to see the 'get tough' policy through.
He said the council was reacting to what people all around the country wanted.
He said applicants who had convictions going back over five years would perhaps be offered 12-month probationary tenancies.
The proposals will be discussed by Anglesey's housing committee this Thursday.