Ask HN: How do I raise my rates as a contractor with an existing client?

I make $80/hr as a contractor. Initially I asked for $100, but I was offered $80 and I accepted. We signed a 6-month contract in August which ends next week. I want to tell them that if they want to renew the contract, I want $90/hr. Is this a 'dick move'? If it is, what is an acceptable way to raise my rates with an existing client?

I should also note that we're not in the middle of any big projects at the moment, so I'm not holding any previous work I've done hostage. All big projects have been completed & delivered.