Communication is meant to present in general terms the concept of online safety for the younger Internet users, children up to 13 years old, whom I have named with a play-upon-words in Romanian, difficult to translate in English (dwarf+Internet user). The paper does not deal with aspects in favour and against dangers of the Internet. But it is certain that materials with harmful content do exist and for the online safety of children some rules are necessary, as we have briefly enumerated at the end.