We consider sets arising from a single word by parallel deletion of su
bwords belonging to a given language. The issues dealt with are rather
basic in language theory and combinatorics of words. We prove that ev
ery finite set is a parallel deletion set but a strict hierarchy resul
ts from k-bounded parallel deletions. We also discuss decidability, th
e parallel deletion number associated to a word and a certain collapse
set of a language, as well as point out some open problems.