Reducing notice period

[Hackney]

I've been offered a job so will be handing my notice in tomorrow or Tuesday. My contracted notice period is 3 months but I'd like to reduce that. Any suggestions as to how?

Pros
I could have everything handed over within a matter of weeks
My company could recruit a replacement quickly (they have done in another department)
Our technical dept was two people, one person left a couple of months ago, while she was working her notice the manager of the dept resigned giving two month's notice rather than three even though the dept was losing both staff. One replacement has been recruited and is working for the co. now.

Cons
There's no-one outside of my team who could take on the work
My account manger - while very good - has been in the job since April and isn't that experienced. She's also on holiday for two weeks in October

Any suggestions?
Obvious answer is to ask and negotiate, my contract is 3 month's notice so I should live with it.

[Hackney]

Due to a couple of things - slight delay in the paperwork from my new company; me being out of the office today and my boss (the MD) being on holiday next week I had to send my notice on email.
The main reason being to get something noted whatever happens.

I've suggested a date in 6 weeks which would certainly give me time to hand everything over and takes into account one of my team being on holiday for two weeks in October.

The boss replied but just to say, "You know I'm on holiday next week (I didn't until yesterday). Let's have a meeting when I get back. I want to know the reason you're leaving"

So hopefully room for negotiating then.