Can the cougars read the stamping on the casing or do you have to yell out that they're FBI 158 grain's (wasn't aware the FBI started reloading/making available their own brand of ammo) to discourage them as you put it, just curious....(I'm just playing with you).

Federal did make a 158 grain +P in a 38 at one point however.
Cheap 38 Special Ammo For Sale - 158 gr +P LSWCHP Federal Law Enforcement Ammunition In Stock - 5f0 rounds
PS: After the Miami shootout and resulting creation of the 357Sig, they've recently gone back to +P 9mm in a G19 as their issue duty weapon, and some carry .40's, FBI can carry what they qualify on). If you see an FBI agent yielding a wheel gun, in 357 or any caliber for that matter, he's retired and LONG AGO retired, watch his sight alignment, he may be pointing towards you and not even know it. LOL
The FBI has selected Glock Gen 5 handguns in 9mm as their service weapon. There has been much speculation about the reasons for their caliber change.
sofrep.com
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The .357 SIG is a bottlenecked, high-velocity handgun cartridge designed by a collaboration between SIG Sauer and Federal Ammunition Company in 1994. This came about, much in the same fashion as the
.40 Smith and Wesson, as a response to the "poor performance" of
9mm Luger LE loads of the time. Much of this "need" for more effective new handgun cartridges stemmed from the 1986 FBI shootout in Miami, involving two bank robbers and multiple (outgunned) FBI agents. The firearms used were Smith and Wesson Model 13 .357 Magnum revolvers (loaded with
.38 Special ammunition) and primarily Smith and Wesson 9mm semi-automatic handguns loaded with Winchester’s 9mm Silvertip 115-grain JHP load.
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Like I said, I'm just having fun... thanks for your posting, i agree... if I go into the woods, I sure as heck am not taking a .380, the bigger the hole, the quicker they bleed out.
Jen