If a DHV story is explicitly a "DHV" it comes across as bragging.
Women are smart and subtle and will notice slight things that come across in stories.
For instance, a real story...
"So, saturday night I went out for some drinks, and I started hitting on this bartender. Well she really liked me, she was really hot too. So she gave me lots of drinks and stuff, and then I took her home and slept with her. It was great."
That's bragging. It's shallow.
On the other hand, I repeated the story this way:
"this weekend was bloody crazy...."
"why?"
"well me and my mates went for a drink, and it was a pretty good night and shit. Anyway, the Bartender, she had the wonderful idea to give me free drinks all night... which was awesome. Until I had to wake up at 10AM on Sunday morning and go shopping. Shopping+hangover don't mix :/"
This time, it doesn't sound like I'm bragging, and I've also thrown in a mention of friends, which is a quick Social Proof, and the fact that she's hot is implied (bartender usually are), and also it's not like I "hooked up with her", it's strongly implied she was coming onto me, which is always better.
Of course, I know she's going to reply... and the replies will usually go two ways.
"Why did you have to wake up at 10AM and go shopping?"
"Well... she hadn't had any drinks so she didn't have a hangover, and since I was leaving town we decided to hang out for my last few hours..."
Now I've just thrown in another shitload of DHVs without sounding boastful. I probably slept with her (strongly implied), I have some money and an interesting life (leaving town), and she still likes me after our drunken fling (she wants to hang out).
On the other hand, sometimes she'll say "Player, eh" or (last time I used it, she said precisely "You have a way with the ladies, don't you?"
Responding as expected "oh yeah" or similar is a DLV. I respond "Oh no... she was Irish [I'm Irish] too... just a solidarity thing

She was probably missing her boyfriend back home

... I miss European women" Of course that's bullshit, but I've now added yet more DHVs... (implied I slept with a girl who had a boyfriend), and negged the girl I'm talking to (by saying I like what she isn't: european)...
In my methods, I make EVERYTHING I say a DHV. Barely a single statement I make isn't a DHV. It's incredible how quick you can gain massive attraction by DHVing and being Cocky/Funny.
Just find those things that make men attractive. Masculinity, confidence, desirability, etc., etc. And *hint* at them subtly throughout every story you tell.
This natural you refer to. When he's talking to a girl, do you think he's going to say "Man, I remember the time I fucked [name of SHB at school], it was great!"? Hell no. But if he's smart, he might tell some relatively boring story. (True story from a friend of mine)... "One time I was going to this pool party [implied DHVs: good social life, accustomed to partying with hot, flirty women], and this girl [name of SHB at school] calls me up thinking I'm cheating on her. Well I wasn't... I've been cheated on, I'd never do that to a girl. Unfortunately [tell whatever story]"... the girl is mentioned in passing, and everything's hinted at.
Always keep it that way.