First things first. Before jumping into a series of vocal exercises that could easily harm more than help a singer experiencing fatigue, it is important to root out the cause of the problem. Again, keep in mind that every singer is different, with a unique instrument, and with a unique set of demands to be made on that instrument. Applying the generalized principles of "correct" vocal production can result in more problems than solutions.
Rather than write a boring litany of all the possible cause and effect formulae, let me illustrate by creating a hypothetical scenario. Sven the Viking is the lead singer of a metal band specializing in "Nordic Pillage Rock." Sven's band is preparing for a six month world tour and although he is gifted with massive physical presence, the stentorian tone which is his trademark is losing torque with every rehearsal. He wants two things. 1. The strength to sing a show without losing his voice, and 2. the prospect of beginning every show from square one rather then with vocal fatigue held over from the previous show.
Lets summarize what is before us:
Sven is a screamer...If we change that, his fans will pelt him with bottles.
Sven smokes...good luck changing that one, Sven just got out of drug/booze rehab and is clinging to his last known vice.
Sven is a hard worker and has reached his level of success by storming through whatever obstacles were in his path.
Sven has reached the point of saying, "It can't get any worse, I'll try anything." He is receptive to my suggestions and "believes" that what I say will help him.
We start by listening, and watching Sven sing a song. Sven has no problem with support. But as I look at his upper chest and neck, I can see the muscles working overtime. Sven is trying to squeeze 10 pounds of sound through a 5 pound opening. He sings with his chin up and opens his mouth wide by raising his head. All wrong! But the sound and delivery are exactly the same as on Sven's records.
Simply put, we need to find the range where Sven's voice is most relaxed. I start by having Sven lay on his back. Now his head is in the proper posture for singing. (For a full explanation of this, see my entry Vocal Architecture.)
I have Sven hoot like an owl, very lightly and in his falsetto, or head voice. I find that there are 5 or 6 notes that he can "hoot" so we exercise just those notes, first by singing "Hoooo" in a light breathy tone as if blowing across a bottle. Remember, the idea is not to make a great sound, but to get the vocal machinery operating in its most relaxed state. I'm looking for free and easy vibration without the tension present when Sven does his act.
Next, I use the syllable "Voo" and exercise the same notes. I start with the "Hoo" in order to begin the tone with air. This allows the vocal cords to engage in a non-violent way with a minimum of tension applied by the surrounding muscles. (See my essay on this principle here) Using the "Voo" brings the initiation of the tone, forward as the lips form the "Vee" consonant, also allowing the tone to ride on a column of air. Repetition of these relaxed exercises will manipulate the mechanism and allow the vocal cords to vibrate freely thereby providing much needed therapy much as an athlete would have sore muscles worked on by a physiotherapist.
After the upper register feels free, I look for the most relaxed range of the lower voice. This is usually in the normal speaking range. The same principles apply, find the easiest notes and exercise them by beginning the tone on a column of air. The "oo" vowel is very helpful because when produced properly, it is not a loud vowel. I ask Sven to sing "Hoo" and "Voo" as if he were imitating very low level feedback.
Depending on the individual, various other vowel sounds are brought into the exercise regimen. Normally, "oo" and "oh" feel the most relaxed while the open "ah" will tend to expose problem areas. I will move through the vowels from "oo" to "ah" with an effort to letting the "ah" vowel be influenced by the habits of free vibration being learned from the "oo."
This would be the very beginning. If Sven were not able to see me every day, I would record a regimen of exercises as he sings them and hope that he repeats these at least once a day. Progress is absolutely inevitable, IF the work is done. When Sven goes on tour, he will find that he is still screaming his guts out, his fans are loving it, and by sticking to a regimen of daily vocalization, his vocal mechanism will be able to survive.
Of course this scenario doesn't represent the way it's supposed to be according to every teacher I've learned from over the years. But what does Sven care about "Bel Canto" technique? Sven lives in the real world and only a real world approach will get him to the end of the tour.