Nagios: turn off service checks/display on down hosts

I want to to tweak nagios in such a way that all checking stops (with services not displayed, or displayed as unknown) for any down node. Said differently I only want to see one alert for a down host instead of 1 (down) + n (1 for every service). Note that I am interested in service display/status, not only in turning off notifications.

Rationale: we use the nagios firefox/chrome plugin to monitor status and nagios' behavior is too noisy giving readings like these (because every node has 20 services):

3 down, 1 unreachable, 4 warnings, 87 critical

This means that the 7 critical services on up node (the problem is on the service) are swamped in a slab of red services which are critical only because they sit on a node that's down/unreachable. What I'd rather like to see is:

3 down, 1 unreachable, 80 unknown, 4 warnings, 7 critical

Or even

3 down, 1 unreachable, 4 warnings, 7 critical

I have looked in service dependencies but I did not fine a way to describe:
"make all services on a alive-host dependen on the status of the host check".

I found the problem discussed here, where one of the participants thought it was a nagios bug,
and here where one of the participants thought it was "as designed".

As things are, I am just interested in the effect, much less in the design philosophy. Note that this nagios is checking hundreds of nodes, so the maintainablilty of the solution is also important.

TIA and cheers.