Summary: The set of correlation immune (CI) Boolean functions can be partitioned into several disjoint sets depending on the Hamming weight of their output column. We show that the number of \(n\) variable CI functions of Hamming weight \(2a+2\) is strictly greater than the number of such functions of weight \(2a\) for \(2a<2^{n-1}\). This seemingly intuitive result turns out to be quite difficult to prove. The combinatorial structure of CI functions revealed here reduces the enumeration problem of CI functions to the enumeration problem of balanced CI functions.