Abstract: A new class of fundamental input method for computers provides comprehensive access to a collection of data strings through a process of successive approximation. A prefix fragment of a desired data entry is used to generate a properly formed progressive prefix presentation set from the collection. Members of the presentation set are longer than the prefix fragment from which they are derived. Presentation sets are recursively-generated based on selections from the sets themselves where all members of the collection containing the prefix fragment also have at least one member of the presentation set as a prefix fragment. The method thus limits the size of presentation sets to accommodate the display space while allowing comprehensive access to the collection through successive approximation. The input method may be enhanced with add-on acceleration techniques and using auxiliary input methods permits creation of data strings unique from the collection and for expanding the collection.