We study the minimal proportion (density) of one letter in nth power-free binary words. First, we introduce and analyse a general notion of minimal letter density for any infinite set of words which does not contain a specified set of “prohibitedrdquo; subwords. We then prove that for nth power-free binary words the density function is 1/n + 1/n³ + 1/n⁴ + O(1/n⁵). We also consider a generalization of nth power-free words for fractional powers (exponents): a word is xth power-free for a real x, if it does not contain subwords of exponent x or more. We study the minimal proportion of one letter in xth power-free binary words as a function of x and prove, in particular, that this function is discontinuous at as well as at all integer points n 3. Finally, we give an estimate of the size of the jumps.