This article examines the performance of heritage speakers (HSs) on two types of acceptability judgment tasks (AJTs) as well as their corresponding confidence ratings. Data were collected from 75 native speakers of Spanish who were subsequently divided into three groups: Spanish monolinguals, Spanish-dominant HSs, and English-dominant HSs. An AJT targeting morphosyntax (Task 1) showed that all groups were affected by task stimulus, that is, they were significantly less accurate on the ungrammatical items. A lexically focused AJT (Task 2) revealed the tendency of HSs to accept complex words that are possible yet not attested. Confidence ratings on both tasks were very high overall, and there was a significant relationship between accuracy and confidence. Thus, the data question the assumption made in a number of previous studies that HSs suffer from a lack of certainty in their linguistic intuitions. Finally, between-group effects show that the Spanish-dominant HS group was not different from the monolingual group on Task 1, yet there were significant differences between all three groups on Task 2. By comparing morphosyntactic and lexical phenomena on two tasks administered in the same modality, this research contributes to the discussion of vulnerable domains in heritage language bilingualism.