[Asterisk-Users] Asterisk integration with office PBX

[John Padovano]

Forgive me if this question has been asked/answered in another post.
And let me reiterate what other users have frequently said - Asterisk is great, and I really appreciate all the work you folks have put into it. 

How have some of you gone about integrating Asterisk with a legacy office PBX, such that the end-user can use a regular office (digital handset) and dialing is fairly seamless ?
Our end-users are accustomed to picking up their office handset and just dialing a 4 digit extension to reach another staffperson in our office. I'd like to replicate that so they can reach staff in our other (international) offices (behind the scenes, the call would route over IP).

For instance, we have regular NEC handsets talking to an NEC PBX, and an analog line from the PBX to the Asterisk FXO.
I already had our NEC tech set up an access code/alias, such that an end-user just dials 6 and it goes to the analog line going into Asterisk. Asterisk picks up after about 2 rings, and then the end-user is prompted to enter the destination phone number (which would be an e.g. 3 digit number corresponding to a SIP destination in the dialplan).
But this means the end-user has to dial 6 and then wait for Asterisk to pick up. I'd Is there a way to have Asterisk pick up sooner, e.g. without any rings ? Ultimately, I'd like to get it to the point where the end-user doesn't have to pause at all. In other words, they could dial e.g. 6123 and their call would be appropriately routed. I realize that probably involves configuring Least Cost Routing on the NEC PBX, but that still leaves the issue of having to wait for Asterisk to pick up the line.

Any help is appreciated.