public class MyThing
    {
        public int MyThingId { get; set; }

        public int UserId { get; set; }
        public string Title { get; set; }
        public string Address { get; set; }
        public string Description { get; set; }
        public DateTime Date { get; set; }
  }

public class MyThingDb : DbContext
{
    // If I comment this constructor out the scaffolding works
    public MyThingDb()
        : base("DefaultConnection")
    {
    }

    public DbSet<MyThing> Things{ get; set; }
}

<connectionStrings>
     <add name="DefaultConnection" ... />
</connectionStrings>

<add name="MyContext" connectionString="Data Source=|DataDirectory|MyDatabase.sdf" providerName="System.Data.SqlServerCe.4.0" />

public class MyContext : DbContext
{
    public MyContext() : base("MyDatabase") { }...

public MyThingDb()
        : base("name=MyContext")
    {
    }

[Display(Name="Logo")]
[DataType(DataType.Upload)]
[NotMapped]
public HttpPostedFileBase Logo { set; get; }

public
DbSet<MyThing> Things
{ get; set; }
}

//[DbConfigurationType(typeof(MySql.Data.Entity.MySqlEFConfiguration))]
public class NameDbContext
{}