Basic-level terms have been described as the most important to human categorisation. They are the earliest emerging words in children's language acquisition, and seem to be more frequently occurring in language in general. In this article, we explored the use of basic-level nouns in texts of different complexity, and hypothesise that hypernyms with characteristics of basic-level words could be useful for the task of lexical simplification. We conducted two corpus studies using four different corpora, two corpora of standard Swedish and two corpora of simple Swedish, and explored whether corpora of simple texts contain a higher proportion of basic-level nouns than corpora of standard Swedish. Based on insights from the corpus studies, we developed a novel algorithm for choosing the best synonym by rewarding high relative frequencies and monolexemity, and restricting the climb in the word hierarchy not to suggest synonyms of a too high level of inclusiveness.