Although it is acknowledged that internal iterators are easier and safer to use than conventional external iterators, it is commonly assumed that they are not applicable in languages without builtin support for closures and that they are less flexible than external iterators. We present an iteration framework that uses objects to emulate closures, separates structure exploration and data consumption, and generalizes on folding, thereby invalidating both the above statements. Our proposed “transfold” scheme allows processing one or more data structures simultaneously without exposing structure representations and without writing explicit loops. We show that the use of two functional concepts (function parameterization and lazy evaluation) within an object-oriented language allows combining the safety and economic usage of internal iteration with the flexibility and client control of external iteration. Sample code is provided using the statically typed Eiffel language.