For centuries, many people have called for language reforms of English, which vary in approach from the radical (completely overhauling existing conventions) to the conservative (preserving most while removing irregularities).
Phonetic alphabets limited to English do not belong here.
Spelling reforms are attempts to regularize English spelling either by reducing the number of irregularities or by making it completely phonemic.
Such historical proposals include: Subsets are reforms that use a restricted wordlist and grammar.
English subsets include: Vocabulary reforms seek to reform English by changing or restricting its words without changing its grammar.