Options on making pool members go offline more quickly

I have an application owner that is concerned that when one of his servers begins to fail there is still the potential for incoming connections to try to reach that failing server until the monitor marks it down (current timeout is 16 seconds).

 

Aside from setting the monitor interval lower than 5 seconds, are there any other options available? There is no persistence profile nor is there an HTTP profile; it is just a layer 4 VIP (Standard type) with a TCP profile.

 

I hesitate to add too much complexity but I am curious to see what can be done, if anything.