C# naming convention for enum and matching property

I often find myself implementing a class maintaining some kind of own status property as an enum: I have a Status enum and ONE Status property of Status type. How should I solve this name conflict?

public class Car
{
  public enum Status
  {
    Off,
    Starting,
    Moving
  };

  Status status = Status.Off;

  public Status Status // <===== Won't compile =====
  {
    get { return status; }
    set { status = value; DoSomething(); }
  }
}

If the Status enum were common to different types, I'd put it outside the class and the problem would be solved. But Status applies to Car only hence it doesn't make sense to declare the enum outside the class.

What naming convention do you use in this case?

NB: This question was partially debated in comments of an answer of this question. Since it wasn't the main question, it didn't get much visibility.

EDIT: Filip Ekberg suggests an IMO excellent workaround for the specific case of 'Status'. Yet I'd be interesting to read about solutions where the name of the enum/property is different, as in Michael Prewecki's answer.

EDIT2 (May 2010): My favorite solution is to pluralize the enum type name, as suggested by Chris S. According to MS guidelines, this should be used for flag enums only. But I've come to like it more and more. I now use it for regular enums as well.