@SessionScoped does not work when adding @Named

Consider the following bean support:

import javax.faces.bean.ManagedBean;
import javax.faces.bean.SessionScoped;

@ManagedBean
@SessionScoped
public class Counter {

    int counter;

    public Counter() {
        this.counter = 0;
    }

    public void Increment() {
        this.counter++;
    }

    public void Decrement() {
        this.counter--;
    }

    public int getCounter() {
        return this.counter;
    }

}

I created a JSF page that displays the counter value and has two buttons for increasing and decreasing. It works as expected. However, when I add the annotation javax.inject.Namedto the bean, it no longer has a session. The buttons still work (the click is processed on the server side), but the counter value always remains zero. I use annotation because in my real application I need to enter other beans into this one and this annotation seems to be mandatory (please correct me if I am wrong). What is the reason for this behavior? What can I do to get around this?