The first thing that comes to mind is that if you want to use a class with only static methods and attributes instead of a singleton you will have to use the static initializer to properly initialise certain attributes. Example:
class NoSingleton {
static {
//initialize foo with something complex that can't be done otherwise
}
static private foo;
}
This will then execute at class load time which is probably not what you want. You have more control over this whole shebang if you implement it as a singleton. However I think using singletons is not a good idea in any case.