I don't think to cancel several credit cards will have negative impact on your credit records, given that they are all in good standing when you cancel them. There are serval elements in determining your credit score. They are number of accounts, duration of accounts, current balances, etc. On one hand, to have accounts of a longer holding period will increase your credit score; On the other hand, to have too many credit accounts at the same time is always a negative element in determining your score.