We present a hypothesis for a specific kind of code-mixing in young bilingual children, during the development of their two first languages, one of which is considerably weaker than the other. Our hypothesis, which we label the Ivy Hypothesis, is that, in the interaction meant to be in the weaker language, the child uses portions of higher syntactic structure lexically instantiated in the stronger language combined with lower portions in the weaker language. Code-mixing patterns were studied in five Swedish-French/Italian children aged 2-4. The parts of the code-mixed utterances reflected as much syntactic structure of each language as was used in monolingual utterances in the same recording of each child. This uneven development, which is due to different amounts of input of the two languages, can be accounted for by assuming that syntactic structure is acquired by building each language from the bottom up through lexical learning.