Assuming that categorical differentiation is major acoustic characteristics of English lexical stress through binary instead of more complex 3-way distinction, we investigated lexical stress in broad and narrow focus positions and found how binary distinction is achieved by the concomitancy of secondary stress defined by its position and distance in relation to primary stress. Similar results are found in broad (sentence initial) and narrow focus as well. These results suggest that binary categorical contrast is the optimal choice while differentiation is dependent on robust contrast patterns in the speech signal.