In this paper, we tackle the twin issues of obligatoriness of semantic arguments and variation in their expression through a study of Estonian constructions denoting need. The variation under investigation consists in the choice of case-marking, between adessive and allative case, as well as the option to omit the oblique argument. We extracted and coded ‘need’-constructions from spoken and written corpora and used non-parametric classification methods for analysis. We found high rates of oblique experiencer omission in these constructions (nearly 60% across corpora). The most important predictors of overt expression of the experiencer in our models were participant-internal modality and the presence of nominal complements, meaning that both semantic and syntactic factors are relevant. The choice between two overt cases is affected by person, complement type, and referential distance. Topical experiencer arguments do not show the subject-like tendency to be omitted more often, but they are more likely to be marked with adessive case, suggesting that adessive is more grammaticalised as a structural, non-nominative, argument-marking case than the more semantic allative case. Our findings show that oblique, semantic arguments may be frequently omitted, and both semantic and syntactic factors may affect variation in case-marking.