If you tell a story in the form of a "Lipogram" what are you doing?
The "Lipogram" comes from the ancient Greek for "Leaving out a Letter" and as is the case with so many cultural phenomena, the ancient Greeks got there first!
The earliest recorded example was by one Lasus of Hermione in the 6th century BCE. For some reason lost to history, he appeared to have an aversion to the Greek letter "Sigma" and a couple of his works in this vein survive. Other ancient Greek poets followed suit, often adopting the works of Homer, but then the practise appears to have lain dormant for centuries, before Joseph Addison commented on it in 18th century London, although a medieval Bible translation invoking it has survived.
For a while, works omitting the letter "R" were quite frequent in German and Italian - especially hard in the former, as the definite article often requires it.
But the omission of a vowel is arguably even harder, which hasn't deterred writers from attempting and succeeding in this. A prominent example was Ernest Vincent Wright's 1936 novel "Gadsby" which really grabbed the bull by the horns and omitted the letter "E" - a feat emulated by the French writer Georges Perec (presumably not extending it to his own name on the cover!) in 1969 with his novel "La Disparition", impressively translated with the same emission by Gilbert Adair as "A Void". An entire literary movement, known as "Oulipu" dedicated themselves to this intentional restriction.