Aims and objectives: The threshold hypothesis is one of the most influential theoretical frameworks on the relation between bilingualism and cognition. This hypothesis suggests a bilingual cognitive disadvantage at a low proficiency level and a cognitive advantage at a high proficiency level in both languages. The aim of our study is to contribute to the operationalization of the threshold hypothesis by analyzing parental support for L1 and its influence on the cognitive development of bilingual children. Data and analysis: We analyze data from 100 Turkish-English successive bilingual children and from their parents, and investigate the relation between bilingualism and cognition. The data from the children are scores on receptive and productive vocabulary tests and a non-verbal intelligence test (Raven's Coloured Progressive Matrices). In addition, the parents filled in a questionnaire on language use at home and a questionnaire on language dominance. Findings and conclusions: Our study shows a bilingual advantage for those children whose parents use more L1 at home and have higher dominance scores for L1. These children outperform the monolingual control groups in our study in terms of non-verbal intelligence scores. Originality: The originality of the present study resides in the fact that, to our knowledge, for the first time parental support for L1 and dominance in L1 is linked to the cognitive development of the children. Significance and implications: In this way, we can operationalize the threshold hypothesis and get further insights in the relation between bilingualism and cognition. This will allow informed decisions on the use and support for L1 in bilingual families. Limitations: One limitation of the present study is the fact that our sample is only from middle-class families, and conclusions about other bilingual settings are therefore limited.