PCI6034E with BNC-2110 trigger voltage

Hi,

I am working on using the PCI-6034E with BNC-2110 to count the number of pulses within a given period of time. the input pulse has 5V amplitude and ~20ns width. However, for each pulse, there were some tail signals with around 1V amplitude. Will the till signals also be counted? If yes, is it possible to set the trigger voltage of the counter? Any help will be greatly appreciated.

Thanks,