What do we mean by witty? Think Juno: jokey, playful, more complicated language than is necessary to get the point across, with a tinge of showing off of the speaker's smarts. Take, for instance, Septimus's assurance to Chater that he's a fan of Chater's work:
SEPTIMUS: "The Maid of Turkey"! I have it by my bedside. When I cannot sleep I take up "The Maid of Turkey" like an old friend. (1.1)
Here the joke's on Chater: while the poet thinks Septimus is saying he likes Chater's poems, another interpretation would be that Septimus uses Chater's work as a sure-fire cure for insomnia. The odd thing is that, since Septimus is trying to convince Chater that he's on his side, it would make sense for him to lie right out and say he's the man's #1 fan, especially since no one else is around to hear him. Instead, he makes a joke that no one but himself – and the audience – gets. It's as if he can't help being witty even when there's no one around to appreciate it. While wittiness is in some ways a performance art, it also seems like it's a pleasure in itself.