Why won't Jawbone headset invoke Voice Search/Dialing? I have an Aliph Jawbone (original) which worked fine with Sony Ericsson dumb-phones (K750, K810) but on my HTC Desire S (Gingerbread, 2.3.3) I can't figure out how to use it for voice dialing.

The phone can find the headset, pair with it and connect to it.
If I double tap on the Jawbone's call button, it triggers the phone's last number redial and calls a contact; but a single press (which should invoke voice dialing on the phone somehow), has no effect.

With dumb-phones, I would just press the headset button, hear a low-pitched beep, then a higher pitched beep a second later when the phone responds, prompting me to speak. Then the phone would receive the noise I make, and go and do its thing.  

With this Android phone, I don't hear that 2nd beep, so apparently the phone isn't responding to the Jawbone.

Am I going about this in the wrong way? Should I be using the Car Panel's Voice Dialer instead?
* Update *
I've tried the Voice Dialer, and it almost does what I need, but to use it I need the phone out and visible, with the screen on, and I have to tap on the screen to trigger the dialer. 
I didn't have to do this with phones from five years ago.

Note
I am looking for a hands-free solution, so any advice that involves unlocking the phone, staring at it, and stabbing at the screen simply isn't an answer. It would also be illegal under English driving law.

I am considering buying Cyberon's Voice Speed Dial, because that seems to work the way I'd like it to (without needing a data connection to an online speech-to-text service); but I want to check that I'm not missing some daft configuration setting.
This link is a discussion of this issue on the Android Open Handset Alliance Project site.  Users on this page talk about the problem in detail and discuss some possible solutions. I would recommend you star this issue.  If the enhancement is implemented or there is a status change you will be notified and can try again on your phone.