Does Dovecot really provide a 'PUSH' email service? The mobile phone client (standard with SonyEricsson C510, in this case) reported that the server (our Dovecot installation) offered PUSH email service. I hadn't seen that in the documentation that I'd read and had understood the client-server protocol to be a client-PULL service, in that the clients decide which folders to retrieve, and check what messages there are and fetch any new messages. The clients we've used so far have settings for frequency of these checks.
I didn't explore the option further, yet, being unsure whether there was a genuine PUSH service from our server or whether the phone was using a proxy somewhere (not ours) which would provide an intermediate fetch/aggregation/'pull then push' service of some sort - perhaps similar to the public offers from Yahoo etc.
regards, Ron