Do metta practices and anatta contradict each other?

When I was taught the Metta Bhavna meditation practice it was suggested that I repeat the following to myself > May I be well > May I be happy > May I be free Then again repeating the same again to other people. As the practice goes on then this can be dropped for more subtle methods. But this formulation and the practice in general has always struck me as been at odds with the idea of no fixed self (Anatta ). If I am wishing well to myself and others - who exactly am I wishing well to? Who is this 'I' that I am wishing well to? In general do these kinds of metta practice conflict with the annatta doctrine. I am assuming that they don't conflict as they are both fairly central in Buddhism. Given that, how are the two practices reconciled?