Have a friend who speaks American English say this sentence out loud fairly quickly:
Those t's probably don't all sound alike. If your friend speaks like a typical American and you listen very carefully, you'll probably hear this: "Tap testers say wet wader is bedder."
Did you notice the little puff of air after the t in Tap testers? Did you notice that there was no puff of air at the end of wet, and that the t softened almost into a d in water and better?