Since Ure (1971) and Halliday (1985), different measures have been proposed in the research literature as a proxy for investigating lexicon advances. They are called lexical richness measures and are an important tool in assessing advance of the lexicon (Johansson, 2009). This article evaluates three lexical richness measures of progress in the acquisition of Hebrew by Arab students in Israel: level of abstractness, lexical diversity, and density lexical. The corpus consisted of sixty essays written in Hebrew by 9th and 11th graders. The quantitative analysis reveals several findings. First, abstractness increases with subjects' age, as expected. The density test, however, did not show the expected increase in density with age. A likely reason for this is relatively high density in younger pupils' essays, indicating lack of cohesion rather than high linguistic competence. The national high school language curriculum for eleventh graders focuses on connectivity, which causes a decrease in density. Third, the diversity test also did not yield statistically significant findings, probably because this test is influenced by text length, which in the ninth grade still does not enable a reliable test. In conclusion, the lexical measures can be divided into two types: basic tests, that can be applied at any level of competence; and advanced tests, which require a high level of competence. Level of abstractness is of the first type: it is effective as a measure of progress in L2 acquisition even in the initial stages of acquisition, while diversity and density require a higher competence level.