How do I block No Caller ID calls?

I have an iPhone.  I do not want to block calls from anyone not in my contacts.  There are many times I need to be able to get calls from a service provider, a friend of a friend, a doctor, a car repair shop, or someone wanting to consider hiring me - and those people would not be in my contacts - so I do not want to only allow calls from just my contacts.  BUT - I AM GETTING HARASSED BY SOMEONE CALLING WITH "NO CALLER ID" over 100 times a day.  Is there not a way to block "no caller ID" callers?!?  (Verizon has a feature that allows you to do this.  Do I need to switch carriers?)