It is not uncommon to negotiate a shorter exit period when you hand in your notice. I have never made anyone work 3 months because after 6-8 weeks they become ineffective / difficult / disinterested anyway. There is no way I am paying them to **** about.
I currently have two people working 3 months before joining us. I accepted it because I realise they are very important to their current employer – its because they are sh1t hot that I want them! One is due to start soon, he seems to spend about 2-3 hours a day actually doing stuff for me whilst his old employer pays him (bonus for me, stupid employer for holding on to him!). The other called up after a week and said, “Can I come sooner? my boss has managed to get me out in 8 weeks!”).
I previously offered one of my guys new employer a “transition” phase to hand over an employee to them. Basically He’d keep working for me full time for first month, then 3 days a week for second month, then 1 day a week for third month so we could ensure continuity. They hated this idea. I said, OK 3 months full time for me then. He ended up calling back saying, “how about 6 weeks, but you can call him up and “borrow him back” for a day at a time in the first year free of charge”… We agreed. He joined one hour long conference call but never needed him again. The point is there is always a compromise if the people involved are pragmatic.