In some of our projects, there's an class hierarchy that adds more parameters as it goes down the chain. At the bottom, some of the classes can have up to 30 parameters, 28 of which are just being passed into the super constructor.
I'll acknowledge that using automated DI through something like Guice would be nice, but because of some technical reasons, these specific projects are constrained to Java 1.4.
A convention of organizing the arguments alphabetically by type doesn't work because if a type is refactored (the Circle you were passing in for argument 2 is now a Shape) it can suddenly be out of order.
This question might be to specific and fraught with "If that's your problem, you're doing it wrong at a design level" criticisms, but I'm just looking for any viewpoints.