Adding a method or constructor declaration to a class will not break compatibility with any pre-existing binaries, even in the case where a type could no longer be recompiled because a method invocation previously referenced a method of a superclass with an incompatible type. The previously compiled class with such a reference will continue to reference the method declared in a superclass.
Deleting a method or constructor from a class will break compatibility with any pre-existing binary that referenced this method or constructor; a NoSuchMethodError will be thrown when such a reference from a pre-existing binary is linked. Only private methods or constructors may be safely deleted from a widely distributed class.
If the source code for a class contains no declared constructors, the Java compiler automatically supplies a constructor with no parameters. Adding one or more constructor declarations to the source code of such a class will prevent this default constructor from being supplied automatically, effectively deleting a constructor, unless one of the new constructors also has no parameters, thus replacing the default constructor. The automatically supplied constructor with no parameters is given the same access modifier as the class of its declaration, so any replacement should have as much or more access if compatibility with pre-existing binaries is to be preserved.