We study some sufficient conditions of codeword lengths for the existence of a fix-free code. Ahlswede et al. proposed the 3/4 conjecture that Σi=1n a-li 3/4 implies the existence of a fix-free code with lengths li when a=2 i. e. the alphabet is binary. We propose a more general conjecture, and prove that the upper bound of our conjecture is not greater than 3/4 for any finite alphabet. Moreover, we show that for any a2 our conjecture is true if codeword lengths l1,l2,. . . consist of only two kinds of lengths.