[HELP] How to delay start of announcements in Voicemail()

A little problem tuning my installation: When I dial voicemail, or a caller gets dumped to voicemail with

Asterisk seems to get ahead of itself by starting voicemail announcements and playback before they are sent through the channel as audio. This means that the audible password promt or an announcement “the user at extension …” are cut off at the beginning. Is there a global parameter to delay the start of Voicemail()'s announcements?