My experience is the opposite, where booking way in advance will give you often the best deal, if you are using their special offers.
Most airlines have those special offers, where you can book a cheap flight within a specific date range for a huge discount.
I've been doing this for all the "big" holidays and usually ended up with a price that got me the second ticket almost for free, when compared to the normal flight prices.
However, this means you are planning the trip based on your flight dates and not the other way around, which of course doesn't work for almost all non-holiday trips.
Most customers who book way in advance are in one of two classes: really price-sensitive, or really time-sensitive. The airlines try to figure out which you are through the special offers. As such, they'll set the base rate higher than the 3-month out rate to catch some extra revenue from the time-sensitive people, and then have "special offers" to induce the price-sensitive people to book.
Most airlines have those special offers, where you can book a cheap flight within a specific date range for a huge discount.
I've been doing this for all the "big" holidays and usually ended up with a price that got me the second ticket almost for free, when compared to the normal flight prices.
However, this means you are planning the trip based on your flight dates and not the other way around, which of course doesn't work for almost all non-holiday trips.