Fare bucket availability is a necessary but not sufficient condition for being able to book a particular advertised fare. Look at the rules for the cheaper fare you'd like to book and you'll probably see a restriction that your preferred flights don't meet. Likely candidates include advance purchase period, date range, days of the week allowed in each direction for the TATL flight and minimum stay, but there are others.

ExpertFlyer is an excellent tool for researching filed fares and the associated rules. The ITA Matrix will help you put a suitable itinerary together.

EDIT: You've changed your question since I replied, MarJon, but finding the answer for any trip you're considering will still involve looking at the fare rules.